Fenders/Mudguards are more important on a commuter bike than any other style of bike. That's because it helps keep you clean for wherever you're commuting to.
So the features you're looking for in a mudguard / fender are
- Length - a rear mudguard should stop water and muck flinging off the back tyre from hitting you or your bags. To do that, the rear mudguard should be long enough to finish at-or-below the level of your rear axle. The front guard can be even longer because its job is also to protect the bike's BB area from road muck. Its not uncommon to see front guards dropping even lower.
Some have a leather or rubber "curtain" or mudflap that continues down where the guard stops, increasing its effective length.
Also, the front of the rear mudguard should ideally finish below your BB. The longer front stops road-water from hitting you in the face while turning.
Example of an overall excellent design for mudguards. The silver L brackets at the top go into the stackup of your rim brakes, either on the nut or on the brake side. So they will require a bike frame with a brake bridge.
Also see the two stays in a triangle. They help support the guard. Some designs simply flap in the breeze, which lets them rub the tires but does look slightly more sporty.
The guard is also a great place to add reflectors, sticker-reflectors, or lightweight lights.
Good front guard example (note its not well-fitted to this bike, because the stays are curved, and there's an inconsistent gap between tyre and guard, and its mounted so the front edge is too high... it should bend down more on the leading edge.)
- Clamping system - you need to inspect your dropouts and look for a spare hole for mounting the stays. Examples:
The two yellow holes to the left are for stays. Some bikes might have one, two, or even three holes. Some have none.
For your bike, I can't see any but they may be hidden by the trailer mount.
If you don't have holes for mounting, you'll need either P Clips which look like this:
Or you may need to limit your mudguards to those which attach to the stays. Downside of these is there's a lot more unsupported length so they flap a bit, and don't last as long.
Notice this one is too short in the front, and should have a second piece that goes from the brake bridge down to the bottom bracket.
Width - a wider tyre needs wider guards. You should have guards that go further sideways than your tyre so they can catch water flung.
Material and colour - its completely up to you. Steel, Aluminium, and plastic are the two common materials for guards, and you can get combinations like "chromoplast" which is a chromed plastic, being lightweight. Some people have made wooden guards, but they tend to have one curve whereas a good guard is curved in two directions to follow the tyre.
As for Colour, whatever suits your bike. Black, bright chrome, and matt chrome are common, but you can paint them any colour you want. Matching or contrasting your frame to suit your taste.
Less-good mudguards there are times where compromise is required. You should avoid "ass savers" because while they're better than nothing, they're not anywhere near as good as a full guard.
There are some designs that attach to your saddle - I have one and road water still drenches the back of my thighs.
Motor-cross style - these are intended to stop mud from packing up between the tyre and the fork bridge on a MTB. Instead they help ease mud through the gap to be thrown off. No practical use on your commuter.
Further information and reading here: Very basic mudguard question and https://www.sheldonbrown.com/fenders.html