If by car camping you mean driving to a campsite and sleeping in a tent then any car will do so long as it is reasonably reliable.
You will want something with high clearance and maybe AWD/4WD if you want to go disperse camping on BLM/NF land since access is mostly by dirt road which can get rough and difficult if there is weather.
If you want to sleep comfortably in a vehicle then you will need to make some modifications to get a flat sleeping area...can be a simple as a supported board across fold down seats. For that a hatch back or SUV type vehicle is better SUV's being a bit larger will provide more options but people use Priuses.
The next step up is a van which can be fitted out from the most rudimentary level up to luxury RV level with full facilities.