As far as how big you can go at stock height.... Probably around 285 70 R17 is the basic consensus around these parts. Careful asking "What will fit?" because there are usually 5-10 people asking the same question every day. Feel try to do a search, or there are "Stickies" that have the answers.
Now, as for type... You can get a set of Nitto Terra Grapplers, which is a pretty decent AT tire. A set of 5 will run you around a grand, plus installation. Check DiscountTireDirect.com. Best bet is to find a tire shop in your area that matches prices. Bring in a print out, and have them match it.
As for wheels, that's personal taste. Some prefer the stock wheels, and they'll go the route of wheel spacers to push the wheels out a bit and avoid rubbing. Personally, I like to add my own look to my Jeep, and go the route of aftermarket rims that have backspacing to push out the tires on their own. Usually around 4.5" of backspacing is where you want to be. (Stock wheels are 6" or 6.25")... So the lower the number, the further out they'll stick.
I got a set of Ultra Drifters for $650 shipped, but everyone has their own preference.
Currently: '14 JKU
Past vehicles: '92 YJ, '97 TJ, '10 JK