^ true..but you can buy a lot of car for 5-7k, and that makes a big difference (even if you're just getting into it).
OP, ask yourself what type of racing you'd most likely get into? Generally, it'll be something like 75% auto-x, with as many track days as you can get to/afford.
Do you have experience driving cars with different drive wheel configurations? What about NA or FI?
These decisions will have repercussions on how well your car will be adapted to a particular type of racing. (ex: a turbo car with a fairly lax spool time might have a disadvantage if you are racing a tight autox course)
I'd just get out there and start taking cars for drives to gauge what you like (again, it is a completely subjective and emotional thing when you're buying a 'fun car'). Are there any local car clubs around? Go to an auto-x day and talk to them, see what people are running and what they'd recommend.
In terms of mods, I'd recommend sorting out (first to last) --> tires --> suspension --> brakes --> engine.
You'll see the most benefit out of setting your car up to handle and stick well.
It's hard to recommend cars (again...subjective thing).. but I'd probably look to get something rwd, light, mechanically sorted, (an lsd and abs would be helpful too).
If you're into 944's, feel free to pm me for more info (I have an 89' 951), and I have quite a bit of experience with them.