Before I lifted my Jeep I squeezed a set of 33's under it stock, I had to trim the fenders a bit tho. Seeing that you want to take it off roading a bit, I wouldn't go any bigger than a set of 31's (ish) which would allow room for flex.What is the largest tire you can put on a stock jeep and the largest on a mild lifted Jeep.
As for tires after the lift, 33's and 35's are the most common. With a 3" lift I would stick with 33's.... 35's if you got yourself a set of flat flares or something that allows more room.
And as for type of lift... spend the extra money and buy a Rubicon Express... they wont let you down and the ride is unbeatable. (In my opinion)
Also, when going that big on tire size it is usually a good idea to upgrade your rear. 35's on a dana 35 is a ticking time bomb.