AT, MT, P235, R17, LT315 - there sure are a lot of letters and numbers when looking at what types of tires may be best for your vehicle. And if you are not sure what you want or need, then things can get confusing pretty quickly. Are all-terrain tires the best, or mud-terrain? What about tread patterns and tire size? Will all tires fit a Jeep's wheels, or are different ones required as well as a body lift or lift kit?
Yes, changing or upgrading tires can be quite the daunting task and the first thing to do is decide your Jeep's primary use. Is it a daily driver with limited off-road exposure? Or is it mainly an off-pavement adventurer? Perhaps a mix of both? Most people will find themselves in that first category, and as such should look for tires that perform well at high speeds, while also giving performance in moderate off-road conditions - in other words an All-Terrain tire. These tires are typically quiet and perform well around town and the highway, but still have enough aggressive tread to tackle modest types of trails. These types of tires also have good tread life and can usually get 40-60K miles before they need replacement.
Mud terrain tires are just that, tires designed to get your Jeep through mud, over rocks, or past may other types of off-road obstacles. These tires use a softer rubber compound, allowing the treads to dig into the ground and propel forward easier than all terrain tire versions. Plus, the treads have wider gaps allowing the tire to 'grab' mud, snow or other debris and push them out of the way. Mud terrain tires also have a stronger sidewall than other tires, which helps prevent punctures or tears when the tire is up against rocks. While you can definitely use a mud terrain tires on road, they are quite a bit louder than all terrain and its soft construction makes for a faster wear. They also reduce your vehicle's fuel efficiency versus all terrain tires.
Once you decide what type of tire fits your needs, choosing the correct size is just as important as not all tire sizes will fit every rim - especially when you are upgrading size. But if you are just replacing your current tires, the easiest way to verify what you have is to check the tire sidewall. For example, on a 2015 Jeep Wrangler Sport, the tire may read P225/75R16. Breaking that out, the 'P' stands for passenger tire and this may also read LT (for light truck) on some tires. The 225 is that tire's width in millimeters and the 75 is the tire aspect ratio - relationship between the sidewall height to width. The R (for radial) should always be standard on just about every tire, however some may list 'B' for bias meaning the tire's body cords run diagonally across the tire instead of radically. Bias tires are designed for off-road only use and can be dangerous if used on pavement because of its construction. Finally, the 16 indicates the tire's diameter so this particular example means it fits a 16" wheel. For more information on reading these measurements, you can check here. Also, some tire manufacturers list their tires in inch measurements instead of metric, so here is a handy conversion chart.
If you are looking to improve your vehicle's off-road capability, or give it a tougher look, then larger more aggressive tires are certainly on your list. However, in doing so, you probably will need a suspension or body lift to accommodate the larger tires. You may also need to change rims as well because a larger tire in the size you want may not be offered in your vehicle's current wheel size. Other modifications may be needed as well and you can check here for further information.