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I'd say the best bet in that size would be the Hankook RS-2. It's the only seriously competetive street tire class autocross tire in that size. I haven't had any myself, but a bunch of the guys that I autocross with have had them and quite liked them. There's a better selection of tires in the 225/45/17 size, where you can get the best street tire for autocross, the Falken Azenis RT-615. 17x8's will be fine for the 235's. That's the wheel size I've got and I think for my next tires I'll get the RS-2's in the 235 size.
Of the two you listed, my vote would be for the Goodyear F1. I have a couple of friends who run those, i've driven on them and was very impressed.
As to the Hankooks, i have a set of the R-S2s on my FD and they do great on the track as well as the street. I got mine from edgeracing.com for about $100 apiece in 245/45-16 and would recommend them very highly. I don't like Dunlops for the track as they tend to chunk fairly easily. I've never had a set myself, but regularly see people who run them having wear problems. For the street i'm sure they're fine, but i wouldn't buy a set for track use...but that's just my opinion.
'93 Montego Blue w/ touring pkg, 5spd
PFS intake, PFS smic, PFS full 3" exhaust, PFC w/ Commander, 850/1300cc injectors, Mild streetport, aluminum flywheel, D2 coilovers, ACT HD clutch, B&M short shifter, Koyo rad...and lots of other fun stuff = a bit over 300 whp with stock twins and handles like it's on rails