School me on NHRA drag racing classes...

The only competitive drag racing for you is bracket racing. NHRA class racing is simply too restrictive and expensive for hobbyists with our street-driven cars.
Bracket racing is a lot of fun - for both the slow and the quick. If you're one of the slower cars in the bracket, you'll get a thrill from holding off a hard-charging quicker car. And if you get to be one of the quicker cars, you'll get your thrill by chasing down that slower car that got the green and left before you did.
Suggest you concentrate on getting your car consistent from pass to pass and perfect your starting line routine to cut the best light possible. The entire key to bracket racing is a quick reaction time, good launch and consistency.
Get out there, learn the ropes, and have fun!