the difference between a sticky race tire and a wide street tire has to be driven to understand. A 340tw (street) vs 200tw (performance) vs 50tw (race) in the same dimension will a substantial increase in handling.
If you are starting out, get an 8" wheel and put on 225. Look for a tire with the section width & tread width within a inch of each other. Tire rack is good about showing this data. It will also give the optimal wheel width.
If you want more traction get a better tire not a wider tire.
A smaller diameter tire will accelerate quicker but require shifting sooner. On track, a smaller tire gets you out of the corner quicker so you have a higher starting speed for the straight.
In autox, a smaller diameter wide tire will accelerate quicker and have less tendency to slide so you can stay on throttle longer.
A bigger diameter (taller) tire will have a higher top end speed and extend the maximum speed per gear. However it'll be slower to accelerate. Unless you are planning on 150mph on every straight, a taller tire isn't really helpful on track.
Stuffing the maximum size tire in the wheel well is for aesthetics. Getting the lightest stickiest stiffest tire will have the biggest effect on track. Having a properly tuned suspension will enable using every millimeter of that tread width.
If you can only buy one set of wheels and tires, buy for your 90% use case. If you start tracking alot, your consumables cost will convince you of the wisdom of having a track only setup.
