How much space does a cat need?
http://en.allexperts.com/q/Cats-1606/2008/9/confined-area.htm This guy keeps his leukemia positive cats separated from other cats, with some in rooms as small as 10'X10', and I've had 2 cats before living in my room (12x18), and they had access to the master bathroom through a cat flap I had installed in the door (8x10), but I also spoiled them, (9 ft cat tree/toys/interacted with them a lot) and they seemed really happy.
I did take them outside occasionally on a leash which they liked. From what I saw they were pretty happy, if you're limited on space try to add more vertical space for them to play or hang out on, bookshelves, cat trees, or hammocks/perches attached to the roof (doesn't need to be girlish or look like it's owned by a crazy cat lady, I'm a guy and my room is pretty modern looking), just give them more stuff they could do when you're away. Oh yeah try to keep it clutter free, it gives the impression of more open space/less confined.
What is a good pet if you do not have much space and cannot have rodents or bugs or things that need a heat lamp?
It depends on how active the cat is, but usually most pet cats are free to roam most or all of a house. Cats, especially ones kept indoors, need a little space in order to run around, play, and exercise. Large scratching posts are ideal, but anything can be made for the cat to play on or in or around. When at rest, cats take up very little space as they curl up.