there is a ton you can read on this and no one is going to be able to give you a few words that just make it all click, unfortunately... suggest reading this because it gets at your question directly...
Tire Test: The Quick and the Tread - Comparison Tests here's a good reference for tire codes
Car Bibles : The Wheel and Tyre Bible Page 1 of 4
re the question of width, the goal is contact patch... that is going to relate to how inflated the tire is, width, weight of vehicle etc... from there, you need a low treadware rating to increase friction with the road/track surface, and then you need a suspension that keeps the tire planted against the road - read about that here
Caster, Camber, Toe and here
http://www.carbibles.com/suspension_bible.html