Nice frame! I'd put it on paper before selecting an engine to ensure you maintain a functional power to weight, or go with the most hp you can afford. Remember to check prop sizes for ground clearance with your engine mount. It would be good if you had a flat bottom wing trainer to do it with. Just unbolt the landing gear and bolt the vehicles chasis there making sure you keep the CG around where it should be (plane pilot should know all about that).

Initial development should really be to just get it a few inches off the ground while tracking a straight line. Are you going to leave the vehicle's drivetrain intact or just use its steering? You could hook your steering servo on the car to the planes rudder channel that would be cool.

About your budget, you better get your parents to shell out some cash cause you'll need it, tell them your learning fundamental elements of physics because you want to get into the aerospace industry. Maybe they'll hook it up.