Tires are more of an opinion than anything. everyone has there preference, likes, dislikes, ecad. Lets hear em.
Sizes
All tires have a size. Most smaller tires have a Metric size, like P215/75hr15
The HP strands for passenger, the 215 is the height, and the 75 is the profile of the tires side wall/ tread width ratio, the r15 means it goes on a 15" diameter rim.
Standard tires are labeled like 33x12.50r15. This means 33" tall, 12.5" wide, and a 15" rim.
The width of the tire is what determines the rim width. For most 10.50 and 12.50 wide tires, an 8" wide rim is ideal as it holds the bead on real well. This again is all personal preference.
Picking a tire
There are many things to consider when choosing tires. Will the vehicle be used mostly on road? mostly offroad? what size do you want? what size can your axles handle?
For this area, wheelin is a mix of rock and dirt. Out in the midwest, there is more mud, and the left coast, flat rock with little dirt.
All-Terrain 
these are a good tire if your jeep is a daily driver and you want something that is better on the road. There inexpensive, quiet, and last better longer than some other tires.
They do hold mud, and the sidewalls are quite week making it less desirable offroad.
Mud Terrain.
Mud terrains are a true All-Terrain tire. They do ok on the road, and they do ok offroad. These are tires like BFG Mud-Terrain, Goodyear MTR, ect.
They do wear faster on the road, and they are louder than the All terrains, but they don't hold mud as much, so they have better traction offroad. As some put it, these are a good compromise tire.
I personally like the Mickey Thopmson MTX. I have a set and they work very well. They were about the same price as other tires and have simular tread. They have siped lugs, and are much quieter on the road compared to many mud terrain tires.
Swampers
http://www.intercotire.com
Swampers where originally made for mud. Their tread pattern allows for quick cleaning of mud. This is good as it will keep traction high. Some where along the line people figured out some swampers are good for rocks also.
This a list of what swampers are good for what:
SX- good in rock and mud. Bias ply, great sidewall.
LTB- simular to SX's in performance, but size is limited to 34" tall.
Boggers- Great in mud. They have a paddle like tread. They offer No lateral traction, so sliping sideways will happen.
Irock- Swampers rock tire. Great traction on rocks, great tread pattern, good sidewall. Plus they come in 20" rim size for the guys running portals.
Krawlers
Now if all you do with your jeep is wheel in the rocks, these are it!
Krawlers are made by BFG, originally used for competition. They are only available in certian sizes, 35x13.5r15, 37x12.5r17, and 39.5x12.5r17.
These tires hook up on the rocks like nothing else out there. There drawbacks are they will wear very fast on the street due to the soft tread compound, they are very $$, and the limited sized/ rim size.
There are 2 kinds of Krawler in the 37 and 39 size, a Blue label, which is Dot approved and has a slightly harder tread compound, and the Red Label, which are not DOT approved. The Red Labels are a softer compound for competition use.
All 35's are Blue label and DOT Approved.
This is just the start. Just the basics.
Now lets hear who likes what for what reason.