This might sound kinda weird but....even in an apartment you can raise at least 1 kind of meat animal: Guinea Pigs, called cuy. They are small and gentle, the meat tastes a bit like squirrel (very tasty done with Shake N Bake). Don't let the fact that in this country they are primarily considered pets; chickens are often kept as pets too, and I haven't run across too many people that refuse to eat them because of that.
Hey, back atcha. Too bad about the no animals rule. There are so many restrictions now days when you rent. Especially if it is run by a rental agency. Some places you can't even have potted plants on a terrace. Once you have children that SS gene kicks in when you are thinking past yourself. You'll get a plethora of ideas from this site. Welcome.