John, there's no need to modify your car for trying out autocross at all. Run it as she is and see if its any fun for you. I've run my '65 Datsun pickup with OVR-SCCA just for the hell of it.
My car is quite built, but there's not really even a good class for it anymore. I haven't bothered being truly competitive in many years, and just see if I can have fun. You can run with Buckeye Miata Club at the Circleville Raceway Park (go-kart track), or OVR-SCCA at National Trails in Hebron, or there are some Cincy groups, or I go to SWVR-SCCA in Parkersburg, WV or Charleston, WV sometimes.
The flat black one in Chillicothe has a long history. It's a 1602 that once belonged to Karl from Yellow Springs (a54atii) and it was a pale yellow he called maisgelb (not original) but once looked decent. He sold it to an OU student, that drove it in winter and wouldn't really wave at me when I waved back in my 02. Then that guy ran it into a pole in winter, and sold it to Jacob for cheap. Jacob replaced the front clip and painted it flat black, and he went to OU for a bit. I think I gave him my old 4-speed, some wheels from my miata, and I think he rebuilt the engine with a 2.0L and a head that I gave him and lots of parts from Karl. It was pretty rusty and beat, though. We lucked into finding a fading verona red 02 in a storage unit in Athens though. I wasn't interested in another, but Jacob opted to sell the black one to his friend Garret that was still living in Chillicothe and paid like $500 for the mostly stock red one. I don't know the status of either right now, but think Jacob moved back to Chillicothe and he got a Smart car too.