Since you have an STi I'll quickly assume tire cost isn't an issue. I will also go with your decision to buy the Hoosier instead of pointing you toward anything else. As posted earlier, the difference between the A3S03 and R3S03 are in rubber compounds. The A is for autocross, and will come up to temp quicker, but not last as long. The R is for roadracing and will take (a little) longer to come up to temp, but last (a little) longer. The A and R3S04 is a new tire with steel belts instead of fiberglass. So they are heavier. Durability is the main difference according to Hoosier. Compounding is supposed to be the same, but folks still prefer the S03 over the S04. As supply of the S03 diminishes for a given size, only the S04 will be available, so some are buying up the S03 while they can. If that's what you'd rather have, get em soon. They are slightly faster from most accounts I've seen, heard and read.
You can autocross on the roadrace compound, the difference will be negligable unless you're actually using every ounce of performance from the tires. If you co-drive, it may be better to have the R3S03(4) for longevity. If you do any trackdays, you'll be glad you have R3S03(4), but will still likely burn through a set in a day. That's what...$900 roundabouts..... If you autocross them only, you'll need a set a season unless you're competitive, then you'll need 2 sets. If you co-drive and are competitive, you'll need a steady supply.
Hoosiers are to autocrossers as CRACK is to junkies!
If you have any doubts about other tires, do more research before buying. Until the recent trouble with the Kumho V710, there was actually a choice in top tires for once (that I can remember). There are other options that may or may not be more suited to your needs.
Hope this helps,
....looking for the next Hoosier fix....