I bought a mid-pack Honda ITC car (really back of the pack, but there's a chance that the guy I bought it from might be reading this, so mid to back pack car). I spent around $3,000 to buy the car from him. It was a car that had been raced at Waterford for a few years, so it would easily pass Waterford tech inspection. The tires that came with the car had really only enough tread for driver's school.
I spent around $1,000 for misc. parts for that first season. Paint, because I couldn't stand canary yellow. Obnoxious green is much, much racier. New brakes. Had NASCAR style door bars added to the driver's side for additional safety. Replaced the transmission (wouldn't stay in 3rd gear). And had to work out some engine idle problems - tune up and some vaccum line issues.
Tires. ITC races on DOT slicks, so Hoosiers are the fastest at $800 to $900 per set. I think for Spec Neon you have to run shaved Toyos. They are cheaper. Around $130 each??? At Waterford in the Honda, I totally used up four tires and went half-way through two more. The next season I got faster so I needed eight tires per season since then. So my tire bill was around $1,800. The Spec Neon guys can give you advice on that.
The second season I spent my racing budget on tires and repairs. Already had all the gear, trailer, car, etc., so the racing budget could go into things that I broke or wanted to upgrade. New wheel bearings. New fender, door and paint job. Funny enough, I got hit by a Neon.
Third season I spent the racing buget on tires and upgrades. Engine rebuild. Front and rear suspension rebuilds with new bushings. New shocks and better springs. My driving skill were beginning to catch up to the car. What I mean is that my lap times were beginning to get really consistent. The car was the issue now and less of my speed issues were me. Oddly enough, now that I have moved to Spec Miata, I am again behind the car. The driver is the biggest barrier to going faster. So my approach was build the car myself with good safety gear, all the suspension and handling goodies available, but buy a crate motor vs. a pro built motor. Once I catch up to the car and can run consistent 1:19 lap times, I'll be buying that pro motor in an effort to chase consistent 1:18 lap times.
Things to ask when looking to buy your car:
When was the last time it was raced and is the log book current/last tech inspection?
How many sessions on the engine and how often does the class tend to do rebuilds?
How many sets of tires does it come with and how many weekends do they tend to get out of them?
For front drive cars, when was the last time the front wheel bearings and hubs where changed? Rear too, but they tend to last longer.
What rules changed does the seller know of that you'll have to update (safety wise) for this next season (expired seat belts, side net requirements for NASA, etc.).
Knowing that you are buying a used car for cheap, what did the driver always want to upgrade, but never had the time or resources to do it?
Good luck. Once you get a car, I can help you with some budget friendly ways to approach handling and alignment changes.