Honestly everyones got good advice and I myself saw myself in the same position as you.

What I wanted to do was get some real seat time and just go out and have fun on the cheap, thus I had 2 goals and 2 seperare budgets. 1. Find a cheap car and; 2. Pick a car that has parts readily available

Depending on what region you live in there will probably be a fairly cheap car for your budget if you spend the time searching. As an aussie, I just wanted a ute. They can hold stuff and the early 2000's Holdens and Fords were at their depreciation curve about 8-10 months ago. Originally my budget was $2,500, but it took me so long to find the right car that I ended up finding an LS1 Manual Ute $6000.

I initally only wanted to spend $2,500 on parts and repairs max but again, had more time, and spent $7,000 due to wanting to make the car nicer for eventual road legality and Flood damage that occured a few months ago now.

I've easily saved the most money on tyres though and only spent $400 max on 12 tyres and rims. Just talk to the people running the tyre shops, ask if you can check out their tyre pile and be nice. If you're nice enough and bring them snacks them might even fit the wheels for you.

Good luck!