These are the numbers in the manual for the A3/S3. Shouldn't be too far off for the GTI.
High Performance/Summer Tires:
A3
225/45R17 - Unloaded - F=30 : R=28 Loaded - F=36 : R=36
225/40R18 - Unloaded - F=35 : R=32 Loaded - F=36 : R=36
235/35R19 - Unloaded - F=35 : R=32 Loaded - F=36 : R=36
S3
225/40R18 - Unloaded - F=39 : R=36 Loaded - F=42 : R=42
235/35R18 - Unloaded - F=39 : R=36 Loaded - F=44 : R=44
44F and R is what was on my door jam. The ride was just terrible. I dreamed about my CC a many nights, wishing I never traded it in. But one day I decided to look through the manual because I was bored and made this startling the discovering. It changed my world for the better. But I still ended up getting 17's
I have a friend with a 2013 S8 and we both agreed that the ride quality was better in the CC than the S8. The S8 is 1000 times better in ever other way though. Lol.