first time out, don't worry about the car-- if it drives fine on the street/highway, then it's probably okay for the usual autocross day. autocross is about 90% driver and 10% car, so work on the driving first.
when you get good enough, you will probably come to the conclusion on your own that you might want just a car specifically for autocrossing (and most likely that car isn't going to be the alltrac, sorry...) if your budget and garage space and life circumstances allow for it.
go out there first and talk to a lot of the experienced people out there. have them ride with you (get an instructor/volunteer if there's one available)-- they will give you the best tips about your driving and also about car setup in general.
in general, the most important parts of the car for autocross is (in this order):
3. driver (okay, i'll stop... here we go):
4. alignment (a combo of personal preference and driving style and what's good for your car specifically): normally as much negative camber up front as you can get, as much positive camber as you can get, and then about 1/8 to 1/4" toe out front, and 0 to 1/8" toe out rear (some people like toe in-- i like my back twitchy-- remnant of me driving mid-engined cars like the MR2 and Exige).
5. tires -- best street tires you can get for now (when you do enough, you know the fastest guys run on r-compounds, but $$).
6. suspension: shocks first -- best bang for the buck are koni sport (aka "yellow")
7. springs next
8. sway bars
9. brakes (just rebuild/refresh stock brakes, get new rotors, maybe upgrade pads. no need for $$$BBK for autox).
10. other stuff (LSD helps. power mods help but as you can see not as important as you think, it's at the bottom of this list-- start with downpipe/exhaust, turn up boost (manual or electronic boost controller)-- however this will most likely bump you into some class where you compete with really fast cars (modified Evos and STi's to start, i'm sure...)).
enjoy, if you are frustrated, get some help don't quit. unless you really try it a few times and determine it's not for you. i never really planned to autocross my ST185, but since it's my only car now and once in a while i get the itch to race so i just bring what i got. that being said, my car is set up for autocross because that's the way i like my cars to handle and drive. i've been autocrossing for 13+ years now, my favorite car was my MR2 and my Exige, but my alltrac the way i have it set up isn't that bad. it's just a delicate car that i'm afraid might fall apart if i abuse it too much lol.
(better to get out there and "do" it, but if you want to read a bit, here's some good sites):http://farnorthracing.com/autocross_secrets.html
-- a bit technical for some, but *very* good resource for car setup and debunking myths
a site that has links to other sites (very good): http://www.autox4u.com/novices/