It's .9 inches taller than what I have now.

 

You'll really enjoy the RS3s. They've got a lot of grip and are great at transitions. They do ok in the rain on the street, not sure about wet racing though, haven't done that with my RS3s. Cold isn't too bad, I wasn't too far off people running R1Rs end of last season in autox.

And damnit, Tirerack pushed back the 225/45/15 to 5/25 :(

 

Might I poke in and suggest 15x8s if you go down the 15" road. Easier to fit the cheap 205s between track days and still work great with 225s.

Although it is possible to put 205s on 9s still. Just don't rule out the 8s.

 

There is no sense in putting a 225/50/16 tire on your car on 7" wheels. Cancel the order.

a) it's too tall
b) it's too wide for the wheel. For track use they will squirm like crazy under all loads. You will have to overpressurize them to stiffen the bulging sidewalls. Lose. Edit: your fail choice, however, allowed me to use the words "stiffen" and "bulging" in the same sentence in a family-friendly, internet-filter-approved way. Win.

For track use get some 6ul's. 15x8 with a 205/50 tire, or 15x9 with a 225/45 tire. If you must do dual duty with the wheel/tire combo, 225/45 on the 15x8 is a reasonable compromise and works well with the RS3 size availability.