You can do 35 or 37 inch tires if you want, but you don't have to just to give your JK a more confident look.
You can fit 33" tires on a JK --with proper wheel offset-- without a lift, and retain the factory ride and handling.
Unless you really want to lift your Jeep, I suggest a set of 285/70-17 ATs with bold tread pattern like the Goodyear Duratracs, the BF Goodrich KO2 or General Grabber AT2s.
Here's what my Sahara looked like when I picked her up from the dealership vs with AEV wheels and Duratracs tires.
And here she is with the same wheels and tires AND a 2" Economy Lift (i.e., a spacer lift) just for looks.
I don't intend to off-road with my Sahara much; it is my all-weather family travel vehicle. Buying these Duratracs was one of the wisest choices I made: they are smooth, quiet and perform amazingly well in poor weather, and I retained the factory handling; I hear others get similar results with the KO2s and Grabber AT2s.