Welcome to the forum and congrats on your new Jeep!
It would probably be a good idea to post this in the wheels section instead of this section: Tires & Wheels - Jeep Wrangler Forum
It would be better to go with 15, 16, or 17" rims -- The smaller the rim, the less tires will cost. Also, more side wall is better for off road. Larger rims will get damaged easier.
15" choices are limited because many will not fit on the 2012. MB72 is one that will fit. The discount tire rep has a list of all that will work. I went with a 16" rim because I didn't find a 15" that I liked.
18" would be fine if you're going more for looks and don't plan to take it off road. As mentioned, the tires will be more expensive.
As far as tires, do you plan to lift? Without any modifications, 33" tires will fit on the 2012 with no problems on road, minor rubbing off. 32" tires (stock on the Rubicon) would be the largest you could go with no problems.
If you want to do flat fenders, you could do 34 or 35" tires with no lift. Otherwise, you need 2 - 2.5" of lift to run 35's.
Regarding types of tires: What are you planning to use it for? Lots of off road? Or mostly street driving? All terrain (AT) tires are better for street driving and perform well off road. Many prefer the mud terrain (MT) tires because they look more aggressive than the AT and provide better traction off road. However, they are louder on road and wear out much faster.