AEV is coming out with a 2.5" spring lift. You can read about it on their forum and see some photos of Jeeps it's installed on (the thread is labeled "News on the 2" Lift," iirc, but the lift is 2.5".) It will be out within a very short time, maybe even now. The 2.5" suspension won't run money wise what the 3.5" or 4.5" suspensions run. Dave Harriton wrote in the thread that it will cost a little more than Tera Flex's 2.5" suspension, so maybe take look the TF pricing for an idea. On the thread you can also read Dave's comments on the weight carrying ability and other features.
The oem suspension won't carry enough weight, imo. The AEV suspension will carry plenty for your use and for the later addition of bumpers, etc, if you decide you want or need them.
For what you describe as your use, I would be looking at 33"x10.5"x16" or 17" A/T tires, metric 255/85/16 or 17 or so. But the 32" oem Rubicon tires are good tires and you may be able to pick up a set of Rubicon 17" wheels with the tires on them taken off a rig a guy is putting bigger meats on. Search Ebay, or other forums' for sale sections. Take offs are good deals, imo, and you can recoup some $'s selling your 18" rims and tires.
FYI in the AEV forum thread there is a photo pf a Jeep with the 2.5" suspension and the factory Rubicon tires and wheels. Looks good - my wife has a JKUR with the 2.5" TF BB and the oem Rubicon wheels and tires, performs well too. You can run 35's on the 2.5" suspension, but with 35's comes re-gearing. As far as being good in the snow, the oem BFG M/T's on the Rubicons are siped, and they perform pretty well in my experience. They're quiet on the road for an M/T too. BTW, I added totally uneccesary Spider Trax wheel spacers to my wife's rig to bring the tires out to the endge of the fenders. Greatly improves looks, imo, but totally uneccesary.
With 33's, maybe 34's, you'll be fine with the oem tire carrier and I would hold off on bumpers for $'s and until you know what you want and need. BTW, AEV's tire carrier will work with a stock bumper and you can get a 10gal fuel carrier which mounts behind the tire, a nice way to carry extra gas or water, and it accomodates a long handled shovel as well. If you don't have a rear hitch receiver, get one. You can find them for less than $100, they are easy to install and they pay for themselves by protecting your bumper (seems like I come down on mine frequently) and in utility with racks, etc. 35's and you'll either need to strengthen your tailgate hinges or go with a carrier. There are a couple of options for strengthening the tailgate hinges if you go bigger than 33's or 34's. Can't recall off hand who makes them.
You will need a Hi Lift, a good shovel and a snatch strap too. If you travel alone alot, you might want to consider a winch. There are some pretty inexpensive options that will work well and winch plates compatible with the oem bumper are available.
Not all of this needs to be done all at once. The suspension and tires will make the greatest performance improvement for the use you describe. The rear receiver will pay for itself first time you land on it. Hi Lift, good shovel, recovery/snatch strap are really required gear. Ax or bow saw, piece of 3/4" plywood about a foot square for the jack on soft ground. A decent enough air pump kit so you can air down and back up as you need to.
The air damn skid is not so neccesary for a non-Rubicon. On the Rubicon it protects the electronic say bar disconnect gear, but on non-Rubicons it's a little high to provide much protection to the tie rod, etc. Save the $'s for now and see how it goes. If you find you need one, maybe look at Currie's tow bracket/skid. I think its less $'s than most alternatives.
There's a thread here with a photo of a chop job RoverTrader did on his oem front bumper. Looks great, doesn't add weight and gets the vulnerable ends out of the way.
Definitely yes on the transmission cooler.
Really, a JK serries Jeep is very capable off road. A plain Jane, right off the lot Sport is better than my old built CJ5 from years ago, and that was considered a really capable rig at the time. While I was in Moab this year, I was reminded of how good the Jeeps are right off the lot. I was out there twice, once during Easter Jeep Safari and once in August for a couple of days with my family. The stock Jeeps did some amazing stuff, they are really capable. And when we were out there in August I rented a lifted JKU sport with open difs, just the BLD system, for the day for my wife and hired her an instructor. My kids and I followed them along all day, and there was only one climb, which had a bypass, that we did that they didn't. I'm not sure they couldn't have done that without drama either, but the loose broken rock would have had the BLD working.
Hope this helps,
JPK