You'd be surprised.. I wish I had paid more attention to my math and physics classes in college - racing, more than anything else I've done so far, could really use those skills!
THIS! I need to go back take those courses again.
Collect all your data... ALLLLL your data before spending the $$
My advice would be to approach racing from a more logical and pragmatic angle. Don't race a car you have a previous emotional attachment to. Instead look at the classes and look at your budget and then talk to racers. After that choose which class looks to be the most fun and fits within your price budget. Some classes have lots of competition, a car that costs $10k and $5-8k per year to put together a full season and be competitive, while other classes with great competition could cost you $40k for the car and $40k per year to be competitive all while doing the same lap times. What is YOUR budget? Think about this regularly used phrase, "Don't race the car if you can't afford to leave it at the track."
Going fast on track with other cars might seem fun NOW (and it still is!), but in 3 years, after you've been doing it awhile what you'll
really be wanting is good close competition. The excitement of going fast for most racers pales in comparison to close competition. So if you're going to start this endeavor, start it in a fashion where the fun never grows old. Seek out competition.
Consider the class, the fun, the money and THEN consider the car. It's usually a LOT cheaper to go buy a race car that is already built and proven and the spend a bit of extra dough "freshening it up". Such as bushings, shocks, belts, seat etc...
Looking at "ST" for example. Last year there were 3 cars/drivers that did more than 4 races and finished 1,2 and 3 in the championship. You're looking at an M3, a Turbo 968 and a well prepped STI. The best part is that these 3 guys are excellent racers, builders and mentors and you'd be good hands in ST. But once again, that is if ST is within your budget. Talk to them an find out what it takes to compete in that class.
The MOST important thing about grassroots racing is fun and only fun and all the good things that come from fun.