Advice on whether 370Z is the right car for me...

280z/300zx

The 370z is not HPDE ready. You will need to spend a decent amount on brakes, tires, fluids, oil cooler, etc. Auto-x is no problem. I've done multiple events in my stock Z. It's the HPDE where you are going to have to pay to play.

My thoughts are buy an old car, not a beater per say. You can buy a nice condition 240z/280z/280zx/300zx (80's) for 5k or less. Spend another 1-2k in prep work/parts and have a nice good to go car. Other options are older supras and corvettes. You can get a decent condition C5 Vette for less than a used 370z and for the same price as a used 370z you could get a C5 Z06. Vettes are a lot better preped track wise than the Z is but being that they are used brakes and tires will still be an issue BUT they won't require an oil cooler like the Z does. Personally I'd probably buy a C5 Z06. Vettes are cheap to maintain and fix (relatively) compared to other cars in it's class

That being said, if it were me I'd probably just buy the new car I want and learn driving it. It will have a higher learning curve but it will also be cheaper in the long run rather than buying one car now and another later. Remember, the money you spend on tires/brakes/fluids/oil coolers/etc won't be recouped when you sell.