Well, to be honest, you can't compete nationally. We just don't have a nationally competitive car. To win in such autocrosses, you need either a prepped 1989-1991 Honda Civic Si (Not the Frankencivics either) or a Subaru Impreza 2.5 RS, again prepped. We have a local guy who competes nationally driving a rather stout 2002 Toyota Celica GT-S, who is a damn_fast driver, but it still isn't the right car for the job.
When you get to national events, it's as much (or more) the car than the driver.
That being said, that doesn't mean that you can't enjoy yourself out there.
To prep your car, it depends what your budget is. I've splurged with the suspension (see sig) and got a set of dedicated autocross wheels and tires.
The big thing, though, is what Roger said -- the biggest limitation in my car is between the steering wheel and the driver's seat. I've ridden along in my car with drivers that have several years experience, and I'm amazed at what the car can do. I just can't make the car do that yet, but I'm learning.
