No Civics, or any other front-wheel drive vehicles. Front wheel drive vehicles do not drift, they power slide. Completely different from drifting.
You will need a rear wheel drive car to drift. In a rear wheel drive car, the ***-end will need to slide out when throttle and parking brake are applied, this allows the car to oversteer thus causing the rear wheels to "over take" the front of the vehicle.
I would suggest a Mazda Miata (MX-5), Mazda RX-7, Ford Mustang, Nissan 240zx, Toyota Supra, Nissan 350z, BMW 325i, or the granddaddy of all drift cars, the Toyota Corrola AE86.
Basically, any vehicle that is rear wheel drive will work as a drift car, it just needs a bit more power, some better tires, and, above all, suspension. Be prepared to spend lots of money in any car venture, whether drifting, auto cross, drag, or restoring.