In some cities, trash is included with the city taxes. If so, this makes life much easier. However, if not – you would have to pay for trash. I would assume it is a flat rate, and they support recycling. Do recycle. The cost of recycling is a nominal extra, and could be fitted in with your budget.
What I Do
The apartment building I live in does not seem to require separation of recycling. I am guessing it is done by the trash haulers. I do have a shredder, and put the shreds in a large blue bag along with all of my other paper. When the time comes, I take that blue bag down to the dumpster, and dispose of it. Most of my other trash is dropped down the chute. If the place you live doesn’t benefit from separation, then there is no interest in separation.