What size tires best fill out the wheel wells(2006 jeep wrangler Sahara)?

[JuttyC]

2006 Jeep Wrangler Sahara. I want to make it look better, bigger tires, without lift. What is the best size t fill these hug wheel wells out? I want the tires to stick out some too. I was told 31 x 10.5, but is that enough? expert opinion please? Ay pics would be great!

 

[Starship Pain]

I had a Jeep years ago, it had 31s on it. Filled it out nicely.