A stock Wrangler Sport will do fine off-road as long as you are patient and don't try to exceed the vehicle's capabilities. Your limitations will be your ground clearance, exposed underbody components, tires and axles.
Ground clearance is the distance from the lowest part of the chassis/drivetrain to the ground. If you run over or land on something taller than this it could cause damage if not protected by a good skid plate, and your sport only has minimal protection. So you will need to be cautious if you decide to go rock crawling, boulder climbing or run over logs. But this kind of off-roading is doable with care.
The stock tires are good for on-road and mild off-road driving. They don't offer a lot of grip for rock crawling and don't have the wide-open tread design needed for mud. That doesn't mean you can't drive rocks and mud. Again, it just means you need to be more careful and avoid areas that exceed your capabilities.
The stock axles are light for extreme rock crawling and don't come with lockers. Again, this is a limitation only for more extreme activities. Mild to moderate rock crawling, accompanied by another vehicle that can winch or tow you through more difficult areas, is still achievable.
Things you will be able to do:
* Drive most unpaved, unimproved roads, logging trails, jeep trails, sand roads and firebreaks.
* Drive through mud, as long as you don't sink in to your axles (bring a buddy in case you get stuck).
* Hill Climbs
* Moderate rock and boulder runs
* Water crossings up to headlight depth
If you haven't done much off-roading the best advice I can give you is to join a local club, go in a group or at least with one other vehicle, and start off easy before working your way up. In this way, you can determine what -- if any -- mods you want to make to be able to enjoy off-roading as you like.
Note that it is my understanding that each new Jeep model design must be able to complete the Rubicon trail without stopping for repairs before it can earn the "Trail Rated" designation. This doesn't mean the Jeep won't get damaged -- just that it can continue on without repairs to finish the ride. Nevertheless, this is not an insignificant accomplishment.
