I have konig oversteer wheels. 18x8 and 18x9. I had 245/35 all around. It is too wide for the 8" wheel. Yes it fit, but was not optimal. Now I have a 225/40 on the 18x8 +45 and much happier. My tires are MPSS.
I would get 225/40 for the 18x8 +45.
For under $600 a set, Tirerack has BFG Comp-2, Pirelli P-Zero's, Hankook v12, and Sumitomo HTRZ II of III's (and many more options)
For just above your budget, you could get the Michelin Pilot Sport A/S3 (amazing all season tires) After the discount tirerack has, they are $634.28.
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