Go out there with stock suspension!!!
It might be counterintuitive to you, but there's nothing "wrong" with the stock Neon suspension, it can autocross quite well. For a novice driver, it will be FAR more forgiving than a really stiff suspension. As a bonus, there's nothing to adjust on it, so you don't have to worry about "do I have the swaybars adjusted properly" and things like that. You just go drive the car... which is exactly what you need to be doing at this point.
Lots and lots of info on the FAST site:
FAST - Autocross
Answers to most of your questions, like "do I need to be a member"?
FAST - Autocross
Spend some time reading what's on that site.