If you like using the 8020 stuff many teams use, you can get cheap stuff from the 8020 surplus store on eBay.
8020-Inc-Garage-Sale
I am in no way associated with them, but it's dirt cheap, and it's easy to work with. The tricky part will be hooking up your motors.
Maybe you can partner up with some local mech-people that would love to build you a frame over the summer?? You fund the base, and you get to keep it, but they get the experience building it?
Plywood is the ultimate cheap base. Maybe that is a good idea for your uses?