I've been working on an entry-level robotics project for my school.
I'm sure I don't need to tell you that Arduinos or Raspberry Pis are great, cheap brains.
Frame, depending on what you want to do, can be cheaply made of scrap metal or wood. If you have access to 3d printing, it's possible to print shockingly durable parts using correct infill settings, and printer filament is cheap as fuck. Might check in with a local college, see if you can pay to use theirs.
Motors are gonna be one of those things you'll want to buy new.