i live in an apartment and actually have 2 guinea pigs and a rabbit. we have a pretty big cage that they all live in together in our living room and it seems to work out fine for us. you definitely should bring it to your landlord's attention before going out and buying the pets and their stuff because it can be a lot of trouble finding new homes and things for them if your landlord doesn't approve.
i agree with everyone on doing your research on rabbits because i got my first rabbit this past november for my birthday and i was in for a huge surprise. the cage we keep her in has fairly high walls but an open top.. she's found a way to jump out so we ended up having to zip tie a sheet above the cage so she wouldn't get out while we were gone and chew wires around the apt. they do a lot of chewing, scratching/digging (on your chest if you're holding them, your clothes, carpet), and they need to be let out, as often as possible and under your supervision, for floor time as they need to run around and get their exercise. she's adorable and has a lot of personality (tho IMO, any pet does, if you give it a chance), but can definitely be a brat and be very frustrating. but she doesn't give off any odor/bad smells.. she actually smells really good and "fresh."
and guinea pigs.. they can smell if you don't keep up with cleaning their cage, but are great pets. they don't require a WHOLE lot.. just food, water, occasional treats, and love. they're social animals so they prefer having a companion rather than being alone (make sure they get along).. and they're really vocal, unlike rabbits, so you'll always know when your pigs want attention.
i'd say the cleaner of the two are rabbits. you can also litter train guinea pigs but so far mine will only pee in the litter. their little poops are everywhere else as far as that goes.
either are great pets but pleeeease, i BEG you, don't rush into getting a pet. too many times people do this and realize they aren't ready/able to care for them, so they end up in shelters where they aren't always guaranteed a second chance for a happy home.
good luck!