As for looking after brakes/rims for those of us with rim brakes, it's good practice just to get in a routine of cleaning the bike (or wheels if feeling lazy) after wet rides. Keep the chain oiled, but not too much, so wipe excess (and dirt) off with an oily cloth (old cotton t-shirts are great for this). Regularly run a fold of cloth in between the sprockets, and also wipe the chain rings (front ones) and the rear jockey wheels (you'll be surprised at how much gunk they pick up). Occasionally squirt a bit of lube on the derailleur pivots.
With bikes, just pay attention to brakes and gears - make sure they are cleanish and working.