Lots of great advice here
I've only started to autocross the S this year but have autocrossed off an on for the last 30 years so I can hopefully shed some light on the differences I feel in the S vs. some other cars.
Tire pressure:
For the longest time we always pumped up the tires figuring we would prevent squirm and tread roll but as tires got better it became obvious that we didn't need to compensate nearly as much. With the S I run very conservative pressures and have been able to get the car balanced well after 1 or 2 runs. I start out 34/36 then adjust as the course dictates. Sometimes I'll drop as much as 3 more lbs out of the fronts but usually leave the rears alone. Tuning usually involves getting to the point where the front doesn't push and I can rotate the car with the gas. This last weekend I ended up running 33/36 warm and it was perfect. The tires really don't heat up that much since you get at least 5 minutes between runs for them to cool. it's not like a track day.
Technique:
Smooth on the DE (track) is a great thing. Smooth on an autocross = slow..... Autocross is all about pitching and tossing the car around tight, slow speed turns as fast as you can. High speed in, HARD straight line braking, turn, Hard on the gas kicking out the rear to close down the angle on the turn and power out to the next cone. Done right you steer that car as much with the throttle as with the steering wheel. The Boxster is so easy to rotate (and rotate fast) that it can get away from you quickly so be prepared to over slide and over compensate while you learn the techniques and the car.
Tires:
So far I think the absolute best bang for the buck in the stock classes are the Falken Azenis RT-615's
http://www.discounttiredirect.com/direct/findTireProductCategoryDetailBrnd.do?tpc=FALHZA&tp=Passenger%2FPerformance
So far I have used PS2's and PS N1's in 18" and the RT-615's in 17" (225 fronts) and the Falken's kick serious ass! The PS2's provide a lot of grip but the soft sidewalls make it tough to manage the car. The PS N1's have great sidewalls but are lacking in ultimate grip. The RT-615's have killer grip, stand up well to the heat and have firm enough sidewall to handle the lower pressures. On top of all that they are relatively cheap!
I've seen a number of references to R compound tires but beware, many clubs will put you in the P (prepared) class with those tires and that puts you up against some pretty serious competition. To stay in the Stock classes you need a non-R spec DOT tire so forget about Victoracers, Pilot cups and the like.
And the last thing to remember is you can always learn. For the life of me I couldn't get close to a guy in our club running basically an identical car on identical tires. For the last 2 events he has been as much as 2 seconds faster than me. I'm always second with the next person usually a full second off my pace but he is absolutely unreal. After the last run this Saturday we decided we had some time for some fun runs. He pulls up next to me and asks if I want to ride with him. I learned more in the 69 seconds in his car than I learned in all my 10 runs that day. I learned that the Boxster can defy physics in the right hands. I also learned that it takes a special kind of person to take their closest competitor and show them how to be faster. Porsche drivers truly are a special breed, "There is no substitute"