The 3 racing d4 kit is a great drifter, but its not designed to run normal touring tires.
as far as tamiya is concerned, their only "serious drift oriented" cars are the ta05 VDF series and tb03 VDS. Both can be made to handle decently with touring car tires, but both have carbon plate chassis, and will get wrecked up pretty bad on rough asphalt.
nearly any touring car can drift well with a set of drift tires. mid level tamiya kits that would make good drifters as well as touring car racers include the ta07, xv01 and tb04. lots of people also run tt01/tt02 cars, but they aren't much less than the other cars once you factor in a few upgrades.