Street tires must have measurable tread depth and no cord showing. Any street car in reasonably good condition should pass this quick inspection without any trouble. You should clean out your car before participating since loose articles are not allowed in the car. It is also recommended that you put more pressure in your tires than you would normally run on the street. You may want to talk to other drivers of similar cars about recommended air pressure.
Some clubs have a noise limit.
Any factory production car will pass the noise limit easily, as will just about any decent muffler system. Cars with leaking or open exhaust system may have trouble with the noise limit. If you run a stock car with no significant modifications, there are no other costs up front for participating. Further, it is common for more proficient autocross drivers to invest in higher performance tires, shocks, and seat belts. Those that have become hooked on autocross have been known to spend even more modifying their cars to improve performance and handling.