I thought I'd add something here as well. For reference, I've done track days for about 7 years and raced (occasionally) for about 4. At the entry level for racing, it's not much more expensive than a track day. I run a 600 and mid to back of the pack, so my tires last the weekend (or two). If I do three races, it costs a bit more than a track day, but maybe only by $100 or so. I run with WERA, so the transponder is eventually an additional cost, but that's free the first two weekend anyways.
Point is, like everything else in the hobby, you make of it what you want. Can you spend "in-ground pool" money? Sure you can. But if you're just wanting to dip your toes into the water and do the occasional weekend, it's really not that much more. You do get less track time per dollar, but the excitement from racing is well worth it.
I do a few track days and a couple races each year and enjoy them both for what they offer.