If your using the stock rim don't go any bigger then 305/70/16.
If you have aftermarket rims go with something like a 33" 12-1/2"
I bet you could fit 35" 12 1/2" if you crank the torsion bars and do a 3" body lift.
I have a 2001 - 1500, I just installed a set of BFGoodrich All-terrains 285/75/16 on the stock rims (7 inch wide). They do not rub at all. I did crank the torsion bars 1/4" before I had the tires mounted, but I doubt I even had to but It raised the truck in the front 1 1/2" I think the 305/70/16 would fit on my truck no problem.