Rim diameter doesn't matter. Only overall diameter matters. Honestly, you can easily fit 33" tires under there now, but any larger is going to require a lift of some type. I would guess with a 3" suspension lift, you could probably fit 35" tires under there as a max.
As far as the "best" ones....it depends on who you ask and what you want to get from them. Do you want mud performance over longevity? Snow? How stiff of a ride? Load rating? A lot of factors to choose from here. There is not a tire that is going to be tops in all categories. You are going to have to choose a brand based on what you want them primarily for. If I remember correctly, tirerack.com has a pretty good detail section on the different brands of tires as well as customer feedback. Definitely look there when deciding on what model you want.