If not chipped turbo noise should be fairly muted, particularly test if you can hear it above the noise level of ordinary radio...if should not be obvious.
Check for any hesitation through the rev range...could point to faulty MAF/AMM...do a search if you don't understand. Check temp gauge acts normally on a 20 min run...should be bang about 90...after 5/6 mins and should stay there when idle or not
On S3s check also for any obvious crunching on gear change...particularly 2nd to 3rd. 6 speed gearbox is not a peach anyway, but should not crunch.
Haldex problems have been known, do a reverse on full lock and listen for any strange thumping/whining...could be haldex.
Check for broken seat mechanisms, check for xenon lights shineing higher or too low...i suppose you need some darkness and garage door for that one!
Check data sticker in boot to see if 210/225 bhp
210 = 154 kW
225 = 165 kW
Ask owners about AVS servicing, where and when and how much they had done. S3 post Aug 2000 need cambelt change at 80k max, pre MY01 officially allowed up to 115k miles!
Look for even tyre wear all round, also same make of tyre front and back...haldex is sensitive to tyres wrt rolling circumference.
If chipped obviously ask where, when and how much achieved...but factor in shorter cycle servicing if you're going to look after it.
all i can think of for now...don't forget there's plenty out there so don't get carried away with the first good one you see.