My son furnished a temporary 4-room apartment for under $100 at thrift stores, some of it very respectable older wooden pieces that I will hate to see him part with when he moves. The shop delivered everything, carried it upstairs, and placed it for him. He’ll get a token amount when he sells it back, so it amounts to a rental for a few months—much better than taking whatever happened to be left behind, in whatever condition.
You can also get a lot of miles out of a few wooden or plastic crates or cubes and some ready-to-assemble particle board pieces.
Basically I did the same thing starting out, except that I shopped my parents’ basement. You can replace things gradually, and there’s always somebody for whom what you’ve got is better than what they’ve got, so you can sell or at least give away your old stuff. Meanwhile you are not sleeping on the floor, and you do get to make some choices. You might even find some gem you’ll keep forever.