You're right not to bother with an F1 car running on a parking lot. It'd be too low and would be too difficult to dial in the handling. I'd look at either the Associated TC4 Club Racer or the new Apex kit if you're looking to just bash and save a few bucks. They are both shaft drive (yes, belt driven isn't terribly problematic unless there are a lot of loose stones...), with lots of parts availability. While the Tamiya cars would be good options too, the Associateds would be cheaper.
If you're dead set on belt drive, I'd look at the 3Racing Sakura XI Sport. It's cheap, has respectable online parts support, and could even be competitive against higher priced kits if you ever decide to race.