PETG is probably what you want. Its very bendable without showing stress marks and in fact you don't even need to mark the bends first.
I bought a unit for WKLaser and Jack Yin, and I'm very happy, especailly with the price. Its a C02 80w with a 24x36" cutting area and it still came in under your budget. But be advised this machine is big and heavy. He has some smaller stuff though so drop him a note. WKLaser here I think.
Jack's service has been very good considering the time zone differences etc.
My laser can cut to any depth, but there will be some trial and error while you play with power and cut speed to get the depth you want.
Thanks
Mike
www.classicplayfields.com