There are only three things a drift car has to have (in my opinion):
-powered rear-wheels (includes AWD)
-reasonable power (>150hp, depending on weight)
-not too much downforce (Super GT cars e.g. are bad)
I started drifting in a Plymouth Superbird just because...it had RWD and I liked it.
There are no restrictions. If there is enough power, you can get it sideways.
There may be a few cars that can't drift, eventhought they have enough power (Veyron), but those are usually cars that you wouldn't even want to drift. If you want an unusual car, there is a thread for that in this forum.