I would look to the Michelin or Goodyear brands as the best mixture of sporty and offroad performance.  My parents also put a nice set of Cooper light truck tires on their stock 1992 Jeep Cherokee 15" rims that turned out very nice -- aggressive tread, don't need to be rotated, and did not need to lift the vehicle to do it.

I have 285/75 16 Kumho RoadVenter AT's on mine. Worked great for offroad, highway, deep standing water, and ice/snow. They're 32.8" tall and about the biggest you can go. They have about 1/4" clearance between the tire and UCA so they rub slightly when turning lock to lock. I have the stock wheels at the moment. Spacers or wheels with different back space would eliminate the UCA rub, but case the outside edge of the tire to rub the body mount behind the wheels. Many people have cut back the body mount, and welded a flat plate of steel over the hole to get the needed clearance. Personally, I just deal with a 1/2" long rub mark on the UCA.

I have a 3" suspension lift so that helps a little, but either way you won't fit larger tires without some work