The butt diameter of the shaft and the size of the grip won't matter too much if you want it to be a standard grip. If a grip is .580 or .600, if it is a standard grip, the installed size will be standard, regardless of the butt size being .580 or .600. The butt size won't drastically increase or decrease the size of the grip. A .580 grip on a .600 butt shaft is 1/64 oversized equal to a midsize grip. In this case, you should have the .580 grip stretched upon installation by 1/2 inch. A .580 on a .620 butt shaft is 1/32 oversized equal to a jumbo style grip.
I change grips every year and only get the standard size. I know a few clubs have a different butt size, but when they get on the clubs I can't tell the difference. There might be a difference of .02, or .03, or something, but I sure can't tell. I have one club that has a .625 butt and it feels a little different, but the size feels the same