Not sure about HPDE or the like but most modded FC's will run in SSM for Solo II/autocross. SSM is a really competitive class, and gets really expensive to be competitive. I'm not sure where to class the 240z, It's E-stock when not modded. Between the two, I would go with the Z. It'll be less expensive to buy parts for and to build. If it were me I wouldn't choose either. Maybe a NA or NB miata or a non turbo SW20. The pignose 240sx would also be a nice choice, if you get the KA24DE in it. I autocross my N/A supra in STX, I drive it hard but it's tons of fun.
If you've never done any kind of sanctioned high performance driving, the first thing you should focus on when setting up a new to you car is making sure all the little things are squared away; such as the maintenance side of the car. Then brakes and tires. Get a nice solid brake setup, maybe some porterfield pads and centric slotted rotors. A sticky set of street tires and lighter wheels will go a long way in feeling what you can and can't do with you're car.
Whichever car or event you choose, have fun. It's easy to get frustrated when at first you see fast guys with fast cars running fast times. All those drivers had to start somewhere. They're were all in your shoes at one point.