Under $10k: I would get an old Volkswagen Jetta, and perhaps get a new muffler; the cars I have seen in my neighbourhood belch black smoke.
Just over $10k: Superformance GT Coupe, or a same-brand GT-40.
Over all costs (things get stupid here): Build a 1967 Corvette body (using another '67 Corvette for a reference) and mount a modern V8 with an electric motor in the chassis (probably from a C4; I'll do research). There would be four-wheel disc brakes and black Motegi wheels, with stamped alloys for winter tires, and the chassis' interior would be stripped and refurbished with lightweight carpeting and less insulation. Bilstein shock absorbers would be used, as would Borla mufflers, for fun. But, it would not make a reasonable daily driver or a track car...