Tire size / performance question

2019 Mustang GT PP1, Roush Supercharged:

Obviously traction has been an issue since adding the supercharger. So I bought RTR Tech 5 wheels. Front 20x9.5 & rear 20x10.5.

1. If I went with a 315 rear, will they fit (no rubbing)? Or would a 305 be a better option?
2. What's my best tire option: daily drving, all weather, GREAT traction? Nitto 555? I still want a tire that will last 30K miles....
3. What size should I go with on the front 265?

***Stock suspension***
 
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