More serious cyclists will ride longer distances, and they may ride in more adverse conditions. I think more serious cyclists should consider sports-specific eyewear.

Some lenses have a gray base tint, i.e. they look gray when you look through the lens. That's considered to be a neutral tint. It affects all colors equally. Some lenses have bronze or rose tints. Both those types of tints increase contrast, i.e. the contrast between light and dark. Borrowing a graphic from the site All About Vision:

Bronze or rose base tints may help you see the last row of letters better. This may be important to help you distinguish potholes or other hazards on the road. Some people might find the tint to be off-putting. Again, you may need to experiment. Personally, as a performance-oriented cyclist, I find that I like rose or bronze tints.

This is likely not that important to the OP's question, but some glasses may be very specific to certain sports environments. Manufacturers may be able to block more or less light on certain light frequencies using dyes. The rationale here is to emphasize colors that are important in specific environments. This is independent of the base lens tint. Oakley's Prizm lenses are one such class of lenses, but I believe that other manufacturers offer similar technology.

This is definitely not vital for most consumers. As a more performance-oriented cyclist, I do like Oakley's Prizm Road lens for road cycling. It was designed for this specific environment. However, it does seem a bit odd when I drive with it, and it does not seem like the best lens in gravel cycling, where the terrain contains gravel, dirt, and tarmac. I mention this as an addendum to my comment above about VLT, because the Prizm Road's VLT is 20%. If you get a lens with very sports-specific light absorption characteristics, be aware of the trade offs in other environments.

It seems like many cyclists see that polarized glasses are more expensive, so they get them. I differ from this opinion. Many of us may not be in heavy automobile traffic, so glare reduction may not benefit us. Cycling on sunny snow days would seem like a use case where polarized might help, but how many of us are actually cycling in those conditions? In addition, we may actually benefit from seeing glare reflected off a puddle - it may help us perceive the puddle earlier. Last, while this may not be a consideration for many, polarized glasses can make your bike computer screen look odd, and may impair readability.

The argument above is, admittedly, taken from videos by Oakley that discuss their rationale for the Prizm lenses - their cycling (and ball sports) Prizm lenses are not polarized, although their water and snow sports ones are. I have no commercial relationship with Oakley to disclose. I am merely a frequent customer.

More serious cyclists will ride longer distances, and they may ride in more adverse conditions. I think more serious cyclists should consider sports-specific eyewear. As a tangential addition, sports-specific eyewear does not require additional retention systems, relying instead on special purpose rubber. In my experience, this is more than sufficient. General purpose or lifestyle sunglasses may not have as strong retention, and users might want to think about a strap if they find their glasses slide off.

Some lenses have a gray base tint, i.e. they look gray when you look through the lens. That's considered to be a neutral tint. It affects all colors equally, and it doesn't affect your color perception. 

Some lenses have bronze or rose tints. Both those types of tints increase contrast, i.e. the contrast between light and dark. Borrowing a graphic from the site All About Vision:

Bronze (synonyms may include copper, orange, or amber) or rose base tints may help you see the last row of letters better. In addition, blue light may affect your eye's ability to see details or to focus properly, and bronze and rose tints block more blue light than grey tints, as discussed at Sailing World. This can help you distinguish potholes or other hazards on the road, but if you are only commuting, this may not be a material benefit. This Wirecutter article contains a quote from Rob Tavakoli, who runs the online glasses store SportRx. He endorses contrasting tints for outdoor activities, explaining that they can really enhance your vision when traveling at speed. However, the site does say that more leisure-oriented riders or commuters should be fine with a neutral tint.

I'm less familiar with yellow tints. They should give some of the contrast benefits discussed above. In my limited experience, they tend to be mainly designed for low light conditions (i.e. pretty high VLT, perhaps 60% and over). Cloudy days would be an example. I don't see green tints offered for cycling eyewear, but I believe they may offer a more neutral color perception and may be favored in some ball sports.

Some people might find some tints to be off-putting. Rose tints do alter your color perception, which may be a further turn-off. Again, you may need to experiment and consider your preferences.

If you can't decide, the safest choice should be a neutral grey base. Personally, as a performance-oriented cyclist, I find that I like rose or bronze tints due to the added contrast.

It seems like many cyclists see that polarized glasses are more expensive, so they get them. I differ from this opinion. Many of us may not be in heavy automobile traffic, so glare reduction may not benefit us. Cycling on sunny snow days would seem like a use case where polarized might help, but how many of us are actually cycling in those conditions? In addition, we may actually benefit from seeing glare reflected off a puddle - it may help us perceive the puddle earlier. Further, while this may not be a consideration for many, polarized glasses can make your bike computer screen or smartphone screen look odd, and may impair readability. Last, polarized glasses may slightly affect your depth perception, as discussed at the Wirecutter article in the last link.

The argument above is, admittedly, taken from videos by Oakley that discuss their rationale for the Prizm lenses - their cycling (and ball sports) Prizm lenses are not polarized, although their water and snow sports ones are. I have no commercial relationship with Oakley to disclose. I am merely a frequent customer.

Side note: altering color perception

This is likely not that important to the OP's question, but independent of the tint, manufacturers may be able to block more or less light on certain light frequencies using dyes. The rationale here is to emphasize colors that are important in specific environments. This is independent of the base lens tint. Oakley's Prizm and Smith's Chromapop lenses are examples of this type of lens technology. Oakley offers Prizm lenses customized to various sports, e.g. road cycling, mountain biking, shallow water sports, deep water sports, etc. Each lens highlights colors that are critical to perception in its sport. Oakley also seems to offer a line of general-purpose Prizm lenses, and Smith's technology also appears to be more general-purpose. Other manufacturers might use this technology, but I'm not aware of them.

This is definitely not vital for most consumers. As a more performance-oriented cyclist, I do like Oakley's Prizm Road lens for road cycling. It has a rose base tint, plus the lens enhances the transmission of yellows and a few other colors (to emphasize lane lines in the road). It was designed specifically for road cycling. However, it does seem a bit odd when I drive with it. In gravel cycling, it definitely seems a bit bright when I'm on gravel (which often contains yellows).

If you get a lens with very sports-specific light absorption characteristics, be aware of the trade offs in other environments. For a commuter or leisure cyclist, I'd recommend holding off from a sports-specific lens unless you know you're committing to the sport. As I mentioned, general-purpose versions of this type of lens exist, which some might want to consider; in fact, I'm trying one out right now.

A subjective disadvantage to sports-specific glasses is that you may perceived as unfashionable or odd if you wear them off the bike. Again, this is subjective issue, and you can do what you feel comfortable with.

How dark are they (visual light transmission)

Sunglass lenses range in how dark they are. Often, this will be summarized by the visual light transmission (VLT) figure. I recall that the darkest Oakley glasses (the only ones I'm familiar with) offer VLTs of 9-12%, i.e. 9-12% of visible light hitting the lens gets let through to your eye. This amount of VLT is fine for very bright light. In cloudy conditions, some riders may perceive those lenses to be too dark. Alternatively, some riders may be more sensitive to light.

Selecting VLT is a matter of personal preference. I have been riding a pair of Oakleys with a VLT of 20%. This does initially seem quite high, but I found that it has actually been sufficient on sunny days. I have a feeling that many people would find VLTs of 15 to 20% acceptable for general use, i.e. they'll be usable on very sunny or fairly cloudy days. However, once again, you should let preference be your guide and you may have to experiment a bit.

One answer mentioned transitions lenses (aka photochromic lenses). These change the amount of VLT when exposed to ultraviolet light, and they can be useful for changing conditions (e.g. you start a ride around dawn, and you ride back in full sunlight). Oakley's literature quotes a VLT figure of 23% for their transitions lenses, which is relatively high, and should be considered. Also, my experience with transitions lenses is that they don't achieve their full darkness (i.e. minimum VLT) unless you're in very bright sunlight. However, transitions technology may have improved since I last used them (around 2015 or so). Transitions lenses are only available in grey base tints (discussed below).

This is not vital for most consumers. As a more performance-oriented cyclist, I do find Oakley's Prizm Road lens to be good for road cycling, but it does seem a bit odd when I drive with it, and it does not seem like the best lens in gravel cycling, where the terrain contains gravel, dirt, and tarmac. I mention this mainly because Oakley's Prizm Road lens has a VLT of 20%, which may seem high, but has been fine in road cycling in practice. If you get a lens with this feature, be aware of the trade offs in other environments.

It seems like many cyclists see that polarized glasses are more expensive, so they get them. I differ from this opinion. Many of us may not be in heavy automobile traffic, so glare reduction may not benefit us. Cycling on sunny snow days would also seem like another use case where polarized might help, but how many of us are cycling in those conditions? In addition, we may actually benefit from seeing glare reflected off a puddle - it may help us perceive the puddle earlier. Last, while this may not be a consideration for many, polarized glasses can make your bike computer screen look odd, and may impair readability.

I would assert that polarized glasses are not clearly necessary for most of us. Getting polarized lenses should be a matter of preference. If you're commuting in with your driving sunglasses, polarized lenses won't really impair you - my issue is with the contention that they are necessary for cycling.

A subjective disadvantage to sports-specific glasses is that you may perceived as unfashionable or odd if you wear them off the bike. But this is subjective.

How dark are they (visible light transmission)

Sunglass lenses range in how dark they are. Often, this will be summarized by the visible light transmission (VLT) figure. I recall that the darkest Oakley glasses (the only ones I'm familiar with) offer VLTs of 9-12%, i.e. 9-12% of visible light hitting the lens gets let through to your eye. This amount of VLT is fine for very bright light. In cloudy conditions, some riders may perceive those lenses to be too dark. Alternatively, some riders may be more sensitive to light. Generally, a manufacturer's product webpage will tell you the VLT of a lens. A retailer should be equipped with this information as well. It's a key piece of information.

Selecting VLT is a matter of personal preference. I have been riding a pair of Oakleys with a VLT of 20%. This does initially seem quite high, but I found that it has actually been sufficient on sunny days. I'm familiar only with Oakley's offerings, and I recall that most of their lenses have VLTs ranging from 10 to 20%. I have a feeling that many people would find VLTs of 15 to 20% acceptable for general use, i.e. they'll be usable on very sunny or fairly cloudy days. However, once again, you should let preference be your guide and you may have to experiment a bit. As noted in some answers, some glasses allow you to interchange lenses, so it's possible you could get multiple lenses with varying VLTs. A side note: some manufacturers may make clear lenses with 75% or higher VLT available for cloudy days or dawn or dusk riding.

One answer mentioned transitions lenses (aka photochromic lenses). These change the amount of VLT when exposed to ultraviolet light, and they can be useful for changing conditions (e.g. you start a ride around dawn, and you ride back in full sunlight). Oakley's literature quotes a VLT figure of 23% for their transitions lenses, which is relatively high. Do consider this. Also, my experience with transitions lenses is that they don't achieve their full darkness (i.e. minimum VLT) unless you're in very bright sunlight. However, transitions technology may have improved since I last used them (around 2015 or so). Transitions lenses are generally available in grey base tints (discussed below), and I'm not aware of transitions lenses with other base tints.

This is definitely not vital for most consumers. As a more performance-oriented cyclist, I do like Oakley's Prizm Road lens for road cycling. It was designed for this specific environment. However, it does seem a bit odd when I drive with it, and it does not seem like the best lens in gravel cycling, where the terrain contains gravel, dirt, and tarmac. I mention this as an addendum to my comment above about VLT, because the Prizm Road's VLT is 20%. If you get a lens with very sports-specific light absorption characteristics, be aware of the trade offs in other environments.

It seems like many cyclists see that polarized glasses are more expensive, so they get them. I differ from this opinion. Many of us may not be in heavy automobile traffic, so glare reduction may not benefit us. Cycling on sunny snow days would seem like a use case where polarized might help, but how many of us are actually cycling in those conditions? In addition, we may actually benefit from seeing glare reflected off a puddle - it may help us perceive the puddle earlier. Last, while this may not be a consideration for many, polarized glasses can make your bike computer screen look odd, and may impair readability.

I would assert that polarized glasses are not necessary for most of us. Getting polarized lenses should be a matter of preference. If you're commuting in with your driving sunglasses, polarized lenses won't really impair you - my issue is with the contention that they are necessary for cycling.