In an attempt to generate more enthusiasm on CEG for autocross, and get more people in the sport in general, I'm going to give some information to those who might be interested.
For an introduction to the sport, try the Tire Rack Novice Handbook. This gives all the information you need to go to your first event.
Autocross is a motorsport where cars are driven around a tight, very twisty course marked by cones (pylons). Cars run solo - thus the SCCA name "Solo II". Solo I is similar, but on a road course. Each run is timed to one one thousandth of a second: xx.xxx seconds. The fastest run is the one that counts. Cars are divided into classes based on modifications and type/performance potential. See http://www.scca.org for details on classing.
There are five classes the Contour is eligible for in streetable form: G Stock (GS), Street Touring S (STS), STX, D Street Prepared (DSP), and Street Mod (SM).
GS allows struts, front swaybar, brake pads, cat-back, DOT-legal race tires, and that's about it. This leaves you with a car with a lot of understeer. However, it's still fun, and will teach you a lot about driving to run there.
STS allows springs, swaybars, wheels, chip, intake, A/C removal, battery relocation, and a few other things, but makes you run on "Street Tires", which has a treadwear rating of 140 or greater. The fastest tires are the Falken Azenis, Hankook Z212, Kuhmo MX, Yoko Advan Neova, and BFG KDW. Max width is 225, on a 7.5 inch wheel.
STX is like STS but allows an LSD, bigger rotors, one high-flow cat (which means headers for us), and wider wheels/tires: 245s on 8 inch wheels. With the LSD and MSDS headers being popular, this could be a fun place to be. It will take some work to fit a 245 width tire, though.
DSP allows the STS mods, as well as LSD, no cat at all, DOT-legal slicks, and an accusump. If I was to build a Contour for track days and autocross, this would be the place to be.
SM allows anything power and suspension-wise without chassis modifications. You can remove more weight, run a turbo, 3.0L, etc. But so can the competition
As I mention in my STS build thread, STS is a good place to be. With the exception of the Accusump, slicks, and LSD, it's everything I'd want in a streetable car. If you're not going to the track much, this is the way to go. If you get a nice suspension kit like the Koni or BAT, a rear swaybar, camber plates, and Azenis, you can be very well-prepared, and have a great-handling and riding street car.
If you go a little more hardcore, you canr have a car that's great on SMOOTH roads, and very, very quick. Again, see my build thread for details.
So, you want to run. No matter where you are, it'll be fun. Let me alleviate a few misconceptions for the wary:
Oil starvation: I run 6.5 qts and I'm fine. Autocross doesn't have long, hard turns, in general. I have yet to run a course that scares me in the least. Just don't run low on oil, and your engine won't break a sweat.
Tire life: a lot of newbies show up unprepared and kill their tires, never to return. If you go too fast, sliding everywhere, you'll not only burn them up, you'll be slow! Erring on the side of too cautious will give you faster lap times, and no appreciable tire wear. Also, make sure you jack the pressures up to 38-40 psi to keep them from squishing and "rolling over" onto the sidewall. This will keep the wear down, and even it out across the tread, as well as making you faster.
Damage: it is possible to damage the car. If you are really nuts, and the course has a flaw, you could do something stupid and mess it up. But, I've never run a course where that could happen. A good course will require serious driver incompetence to have a problem. This is the safest form of motorsport, or very close, as far as car damage goes. The risk is very, very low.
Yes, Buckshot rolled his car. This was not from cornering forces, but from going way too fast on a poorly-setup track and hitting a tire wall. He admits it was really all his fault that he went off - "cold tires, cold track, hot driver", I think he said.
So, go to SCCA.org, find your region, and look for an event! Post up in your regional forum to see if anyone around you want to go too. Read the guide I posted the link too, and have fun!