I get asked this question quite a bit especially by students that just finished a day of Drift 101 lessons.. If I were to recommend a car that is reliable and fun to use, it would have to be the Nissan 350z.
Obviously, there are the staple drift cars such as the Nissan 240sx, but these cars are not cheap anymore and not everyone has the time to find a decent 240sx that hasn't been overly modified.
Before you hit the track in your newly purchased Nissan 350z, I would recommend purchasing a new aftermarket Limited Slip Differential (LSD). Make sure the differential is properly installed and broken in before you hit the track. A couple of other items that help but not necessary (yet) are adjustable front control arms and aftermarket inner tie rods.
Don't forget to bring spare wheels and tires too. Unfortunately, the 350z is limited on truck space, the one thing that I don't like about the Z but with some thought and planning, I have seen drivers bring spare wheels with room for tools and other equipment.
Pay attention to your temps throughout the day. If your car rums dangerously hot after a session, I would suggest purchasing an aftermarket oil cooler and radiator.
Have fun and be safe.