Tire width
 

You could go as wide as you like as long as your wheels will allow it, depends upon how the wheels set, using a deep dish will push tires out further, I'd say 60 series is probly wide as you can get under it. Huge mudders will always require some modifying on a small truck, maybe as you mentioned lift kit, wheels spacers, or fender modifications. I'm a hot rod guy so I always tend to think street racing but I assume you're talking about an offroad 4x4 or similar use. The tire/wheel dealers might can give you a better idea of what will fit under it safely. They likely have some application books on that kind of thing.

I'm running Cooper Maxx ST 265/75/16s on mine. I've got a two inch level kit and 2 inch wheel spacers. They rub. A lot. I cut the bumper back about 3 inches and need to
modify the back of the fender so they'll clear better. You should be able to get away with a 245/75/16 without any modifications other than a small lift and maybe some
negative offset rims. The rims will give you the slight stance you want as well as helping clear fender wells and what not.