Initial D has noting to do with the AE86 being popular. They might not be the most used cars to drift, but they are a drift simbol, it has almost a cult following in Japan.
The most common among the begginers is surelly the S-13, they are cheap and got a robust and powerfull engine, making a good car to pratice drifting.
The FD is no way one of the most common drift cars, it's expensive and hard to drift because of the double turbine. The FC is much more popular, you won't go to a drift contest without seeing one.