Ratpack, I assume that you plan on driving only as a visitor, and that you are not planning to move to the US. If that's the case, then yes, you can rent a car on your British license. If you are moving, it's a different situation and every state has different laws pertaining to timelines for obtaining a state license.
Teri, DH got nicked for speeding only a week after getting his Illinois license. I can say, it's hard to get used to the slower speeds. He just completed his on-line driving school for first-time offenders, to avoid a ticket on his license. Even me, The One Who Obeys the Speed Limit, had to constantly check my speed when we returned.
So Ratpack, have fun driving but it really is hard to adjust to the slower speed limits!