You could take lessons in whatever you wanted, but you would need at least a 3rd class medical to solo, as it has been stated. Also, the Aircraft Owners and Pilots Association has pilot's hotline that you can call for information. I'm unsure if you have to be a member or not, but you first six months of membership are free. TONS of information on anything you want to know about flying and directions to places with information if they don't have it directly.
EDIT: I just thought of the Sport Pilot's licence. You can use a driver's licence to establish medical fitness, and demonstrate safe operation of the aircraft. It's a fairly restricted licence (daytime, good weather, 1 passenger max, also limits on aircraft power and weight), but you're still flying an airplane.