I wouldn't bother changing wheels unless there's something wrong with them or something specific you want that they can't provide. If the brake tracks are excessively worn, then the wheels need to be replaced for safety. The brake track eventually wears down so that the walls of the rim become thin and are weakened. Many aluminium rim wheels will have some sort of indicator built in so that you can tell when the wear reaches this stage. For example, some have a groove machined into the rim and when that disappears it means the wear limit has been reached. I've been riding a lot since 2011 and I've never reached that point on any of my wheels. But I've spread my riding across 3 bikes (2xroad, 1xtri) and 4 sets of wheels in that time and most of my routes don't require a lot of heavy braking. If you're in an urban area and/or you've ridden big mileage you could reach that point much quicker.
I'd stick with alloy rims. If you want to use them for racing too, you can consider a set with carbon fairings like HED Jet Plus, Flos or Swiss Sides. I see no real benefit in full carbon rims. It's a fashion thing.
For everyday riding if you're not looking for anything terribly expensive or fancy there's lots to choose from. For well known mass produced easily available stuff off the shelf, I'd consider Shimano, Fulcrum, Campagnolo, Mavic, DT Swiss, and there are lots more I'm forgetting.
All of these, and other companies offer wheels at various price ranges. The biggest differentiator tends to be weight. You might get a 2000g wheel set for $120, a 1700g set for $250 and a 1500g set for $500 for example. The importance of the weight is debatable. Light wheels feel nice for steep climbs in my opinion but weight of wheels gets hugely over hyped. It's not that big an issue and pretty irrelevant on flat routes. It would make a small difference for sprint accelerations but that's about it.
For general purpose wheels, there are a few things I'd consider:
- Are you looking for an aerodynamic advantage? If you're not racing I wouldn't bother with anything over 35mm deep rims. It's cost without much tangible benefit. There are good 30 and 35mm rims that actually perform reasonably aerodynamically and normal box profile rims won't ruin your day. I use these for most of my riding except on the tri bike.
- Is comfort a priority? It may be worth considering a wide rim (wide as opposed to deep). Typical rims used have a width of about 15mm between the beads (the channel where the tyre sits). The current trend is towards wider rims up to 22mm or so. This allows you get more air volume for a given tyre size and more importantly to get a better tyre profile with larger size tyres (say 25-30mm)
- Do you want the option to go tubeless? Tubeless ready rims will typically cost more. I haven't tried tubeless, I see the merits and if the price difference was reasonably small on new rims I'd probably go that route, but it's not a deal-breaker for me.
- Weight. As above, I don't think it's as big a deal as some do. If my budget allowed I'd pay a bit extra to get say <1600g. I wouldn't pay massive money just to get <1400g wheels.
You may already be aware, but in case you're not - you'll need to check the wheels are compatible with the groupset you're using. Normally this is just a case of checking if it has a Campagnolo or Shimano/Sram freehub.
The other option is to get a wheel built for you. I've never had that done but it could be an attractive proposition. I think Kinlin do a nice 30mm deep rim that's something like 19mm wide and decently aero. A good all-rounder. I'd go with something like that and a good serviceable set of hubs and easily replaced spokes.