I agree with @northvibe. I have tons of PETG for the ramps I make, but if I was going to make a flat plastic for the playfield, I would use polycarbonate (Lexan). Also, that old plastic is probably pretty brittle by now. Don't know where you live, but most major cities have retail plastic stores. Here in Washington, we have one called Tap Plastics. They always have left over pieces of all sorts of plastic that they put in a bin and sell for a couple bucks a pound. When I go in, I usually buy all of the clear 1/8" polycarbonate they have.

As far as cutting it, I may roughly draw the outline of the piece I want to reproduce, then rough cut it with a band saw (fine tooth blade). Then I finish them to the proper size on a bench top belt sander or a Dremel with a sanding drum. If you don't have a band saw, you could also use those diamond dust cut-off disks for the Dremel. If you are really anal, the cut edges of polycarbonate can be fine sanded down to at least 1000 grit and then polished like glass. Can't do that with PETG.

Just ask them which pieces are clear polycarbonate.....they also may have some tinted polycarbonate. Pieces are usually like 12" x 12", so work well for us pinballers making plastics.