Mine kinda found me, although I haven't turned it into challenge car yet. A buddy had an 83 Corolla wagon that he parked ten years ago when the oil pump went south. He sold it to me for $200. The plan is to slap some junkyard panels on it, paint it with a roller, and maybe K-swap it. I do have a Cadillac 500 and TH400 sitting in front of the garage that I'm trying to not just take the low hanging fruit and wedge that in.
Some folks will just buy a ready-to run thing for $1800, like a stock Civic or Miata and throw some 200tw tires on it. They can be very good mid-pack runners. The lady who won the autocross the last time I was there was in a Corolla with some carefully executed mods.
Where do you live? Are you willing to drive? Have a trailer? Some areas like Atlanta, suburbs of L.A., Pittsburgh, and Baltimore have some cheap cars. I have a theory on that. Cities that have a wide separation of wealth (ritzy areas combined with struggling folks) tend to have lower car prices. I think it's because when Dr. Moneybags wants to sell his Nissan for $10,000 in the Ritzyville neighborhood, they have to compete with John selling the same car in Skidstown for $6000. It's also simply a supply/demand thing. Most cities have public transport and fewer cars per capita, which means demand is sometimes lower, but the overall number of cars is high.
My first year, I didn't field a car. I joined up with another team. My second year, captdownshift loaned me his challenge car to take and it was a blast. I found, though, that I loved just showing up as a driver with no team. There are an equal number of teams who really put a ton of work and effort in their cars, and teams that bought a $500 rear-ended Cavalier last week and they are going to throw it in the dumpster on Sunday. That means there are some teams that are kinda in their own competitive world and only let their person drive, and there are also plenty of cars that you can just ask teams if you can drive. I drove a Subaru, a Civic, an Ford Econobox, the Zoomboni, and a few other cars down there. If I ever get off my ass and build my Corolla, I'll toss you the keys and you can ride it like the town slut.
Either way, you'll have fun. I was a complete racing noob. I had never raced other than treeing a Camaro on Maple St. I found that talking with folks about the rules helped me become confident enough to field a car.... once I actually build it.
If you think these people here are great on the forum, just wait and see what they're like in person. Truly awesome people. Take a bunch of old and young, rich and poor, liberal and conservative people, throw in copious amounts of adult beverages, and you would think it wouldn't work, but we're all there for cars and fun, and man do we HAVE FUN. Non stop happy place.
Anyway, back to the topic. Cars kinda find me. I don't even work or hang out in automotive circles. I'm in the Arts. People know I'm a car freak and they tell me about cars for sale or free. I find FBM to be pretty helpful (if not an awkward search format). Craigslist around here is all but dead. SearchTempest doesn't really do it for me because it includes AutoTrader and Carmax and other retail places. I just see the same listings from the cheap sources layered in with retail stuff.