I race a vintage vee. I have not autocrossed it. You won't be allowed to do track days with clubs. Blending open wheel and closed won't happen. You may be allowed to do a test and tune day with a local vintage club or at a road course under other circumstances but they will be few and far between. Check out vintage racing in your area, it's a blast and in our region Vees are plentiful and very competitive.
Vee values run the gamut. A pos car will be cheap and then need a bunch of work to be competitive, reliable and safe. If you are a competent mechanic and/or can do the welding and body work then you are way ahead of the game. Just be careful of that $3,000 Vee that's been sitting for years. You will be much happier with a current car that has a fresh engine. A recently competitive car is for sale in our region with ok paint. $10,000.
My car last summer. Zink C-4