I don't have a lot of RRS-SC specific info for you regarding mods. As for tires, that will depend....what size are you running now and what size would you like to run? Are you willing to consider different wheels? Obviously smaller diameter wheels will allow more sidewall which will improve off-road performance but at the expense of on-road handling. I'm also not sure if you can get a smaller wheel on the RRS due to it's brakes.
Specific tire brands/models? Cooper AT3, Zeon LTZ, or ST-Maxx are all good options. The BFG KO2 and Goodyear Duratrac also are popular. But I don't know if each of these will be available in a size you need.
We really need to know a bit more about your intended use. If it's mostly a road vehicle, running up to Tahoe in the winter, etc, then a good AS tire will be fine. If you're planning to spend more time off-road then the tires I've listed above are pretty good dual-purpose AT options. If you're looking for a serious off-road bias then we can start looking at MT tires but that doesn't sound likely from your post.