My daughter talks about starting a Lemons team when she goes to CSU Fullerton next year, but I think the biggest hurdle is having a place to store and work on the car. If you got that covered, there are lots of <$500 cars in SoCal, you just need to expand your search out of Irvine. Getting a car ready to race is typically about $5000 after you add in all your safety equipment and cage.
RWD and manual is getting harder to find unless you are willing to look at early 90s and older cars. Miatas are great and are easy on the wallet to race as I understand it.
I have raced a '85 Volvo for the last six years and they are rear wheel drive and withstand a lot of abuse, but their manual transmissions are weak. I eventually replaced the transmission with a Nissan 370z manual.
My son is a freshman anteater, I am happy to talk about my Lemons experiences and what we spend every year offline. Let me know and I will email you my contact info.
Team whatever_racecar #745 Volvo wagon