I'm 59, 5'11", 210,and have had a triple bypass. I moved from the flats to the hills, and I want to ride again, but I can't with the gearing I have now. 50/34 chain ring and an 11 speed 10-25 cassette. These hills are really steep, I'm talking "Climb to Kaiser" steep, and I do not like having to get off my bike and finish walking to the top of the hill. Keeping it a double, what groupset would give me the best range and lowest gears for climbing?
What parts are you willing to replace?
You can't get smaller than 34 in the front w/o replacing the crankset with some kind of MTB crank. You'll likely need to replace your front derailleur as well, and there are issues with indexed shifting that you'll need to figure out.
You can't get larger than at most 32t in the back w/o replacing the rear derailleur with an MTB version. There are also indexing issues between road/MTB derailleurs. If you get a road extended cage or triple rear derailluer, you can probably make an MTB 11-32 cluster work with your current shifters.
However, in the long run it's probably cheaper just to get a triple chainring on the front. You'll have a much easier time getting the gears that work for you.
At some point it becomes quicker to push a bike up the hill than ride. Don't let ego override common sense. However, in your specific case where its a hilly circuit, a lower gear makes a lot of sense and will help you build fitness and climbing strength (and save your knees). If at some stage the lower gear is no longer needed, you can always go back to you original gear set, or a set between them.
What you can fit is limited by you dérailleur which has a maximum capacity (Difference in number of teeth from Big Big to Small-Small gears). Typically road bikes will have a short or medium cage - anything from 30 to 37 tooth capacity. We know you have at capacity of at least 31. (50-34) + (25-10)
A new cassette with a larger big cog is readily available - up to the insane range of 10-42. In your case good size to look at would be 11-32 - as its a very common size available at all price points and a big enough range to make a difference. This would need a dérailleur with a capacity of 37. A 11-29 might work as well, won't give quite as lower gear but needs a capacity of only 34, so may fit you existing dérailleur.
You could, go to a single on the front (50) and 10-42 on the back using your existing dérailleur (Roughly same as 34F/29R), or drop to a smaller chain ring for lower gearing. Going single will sacrifice top speed if you drop the chain ring size and have the change in gearing increased between cogs.
Have a look at Sheldon Browns gear calculator to help decide what you need.
I've thought of a different way to approach this problem.
Use an online bike power calculator to get some idea of the wattage you can sustain.
It would be best to do this for a climb that you can do with your current gears and that you know the stats for.
Now put in the stats for the kind of grades you want to climb, and in my experience the maximum sustained grade is the limiting factor. It only takes a hundred meters or so of 18% grade to completely blow up.
You'll get an average speed out of the available power. Now that you know the speed you'll be going, you need to find a gear that is as efficient as possible at that speed.
Go to a handy gear calculator and put in your current gears and see what rpm you would need to ride to match the speed calcutated above.
If the calculator says that you need to ride at 30 rpm or less for the gear you have, thats near the point where the bicycle will be unrideable. IMHO, 60 rpm would be a good place for the average cyclist.
Play around with these two calculators to get some idea of what gears would actually work for you. This kind of approach will save a lot of fiddling around and if you need to make a big change in components, you'll know that at the start.
If your frame and bottom bracket allow it, you could install a mountain bike crank with 42/28 chainrings (maybe Shimano XT). Combined with an 11/32 cassette, that would make climbing really easy.
For the last 3 years, my only bike has been a 29er MTB with a 2x10 drive train and a top gear of 36-11. That's enough for me even on road rides, even when riding in a group where everyone else is on road bikes. (I use slick tires for those rides). I can pedal up to 25 mph and rarely even use the top gear. I love it on 15% grades where everyone else struggles and I'm calmly spinning the 22t chainring.
I ended up getting a 34-50 compact crank and an 11-32 cassette. 34-32 makes it possible to climb most hills without standing up, but I must admit that I spend more time in the lowest gear than I would like.
Do you have any good reason not to get a triple? (I can't honestly say that I did...)