Reading a bunch around the forums is a good place to start. Take a look at photos, get together with some other Jeepers in your area, etc. And just taking the Jeep out as-is is also a great experience to see what works and what you need.
First off, you don't need 4" to fit 35" tires on your JK. You can stick with something along the lines of a 2.5"-3" lift range and be more than capable. Look at Rock Krawler, Metalcloak, Teraflex, Synergy, etc. The better, more complete the kit - the better of a ride you will have. If you're interested in keeping the center of gravity even lower, you can go with just a set of flat fenders and no lift at all.
Second, you can keep the existing wheels, but you will need to get a set of wheel spacers, like the 1.5" Spydertrax. Keep an eye on them every time you do an oil change (or some other regular interval, and you'll be good to go)
As for tires, it is going to be a question of budget, and what sort of terrain you're planning on driving on. Mostly street? Go with an All-Terrain or a hybrid like the Duratrac. Mud? Rock? Trails? Each has their own variation of what works and what doesn't. Some of the more popular all-around tires are the Toyo MT, the BF Goodrich KM2, the Goodyear MT-R, Mickey Thompson MTZ, etc.
Other small assorted items, like axle gussets and a tuner chip will be good, but hopefully that starts you off with a little direction.
Call one of the vendors here if you have questions.
Marcus at River City Offroad 832-526-2415
Jay or Norm at Stomper Offroad
Jason at Krawl
...etc.