Goodyear's MT/R is a superb tire, their current generation which includes kevlar reinforcement is the first tire I've never had any sidewall cuts or punctures while rock crawling.
That tire is essentially a 33x11.50xR16 and for 33" tires, 4" of additional clearance would be a good choice. 3" would 'work' for the street' but for offroading, 4" is better. You can achieve that 4" less expensively than a 4" suspension lift by going with a 3" suspension lift plus a 1" body lift.
Keep in mind that the shock absorbers you'll be installing are the key to the quality of your ride afterward. Not the springs, the shocks. Suspension lift kits like from Rough Country, ProComp, Skyjacker are notorious for their terribly stiff rides due to the cheap stiff riding shock absorbers they include. Stay away from any Rough Country, ProComp ES-3000 or ES-9000, Skyjacker Nitros, Rubicon Express Monotube, or Rancho RS5000 shocks.
Good riding shocks include Old Man Emu Nitrochargers, Bilstein 5100 (not my personal favorite though), Fox, Rancho RS9000XL (adjustable), or the newer Rancho RS5000x which is different than the RS5000 I suggested you avoid above. For the $$$, I don't think the new Rancho RS5000x can be beat. I used to run the OME Nitrochargers which I absolutely loved. Great shock. Then they wore out and right about that time, Rancho pushed me to try a set of their new RS5000x shocks. I pushed back but they gave me a set for free to try after they had noticed me saying how bad their RS5000 was. I have to say I was happily surprised how much I liked and still like the RS5000x. It is a gas (nitrogen charged) shock and it not only has a great highway ride, it also gives great offroad control. It even provides a good ride at fairly high speeds on rough washboard dirt roads with lots of 'whoop's.
Also, cheaper lifts tend to include a "dropped Pitman arm" which should NOT be installed, don't let the installing shop talk you into installing it by claiming all suspension lifts require them. The TJ does not and installing a dropped Pitman arm onto a TJ will screw up the steering geometry which will cause a problem known as 'bump steer'. That causes the steering to be forced left/right as the front suspension moves up/down. 2005 and older model Jeeps and most other 4x4 trucks do require dropped Pitman arms, just not 1997 and newer model Wranglers.
Your factory wheels do have a lot of backspacing which tends to position tires in closer. Your tires are wider than stock so they might rub on the control arms when you have the steering wheel cranked hard over. And once your suspension lift is installed, understand that suspension lifts pull the front axle toward the driver's side and the rear axle toward the passenger side. That can cause the inside sidewall to rub even more. The fix for that up front is a longer (adjustable length) front track bar. In the rear, that can also be taken care of by a longer (adjustable length) rear track bar, or a rear track bar relocation bracket which positions the track bar out further to push the axle back into its 'mostly' centered position. An adjustable track bar makes centering it exactly easy, but the relocation bracket usually gets it centered close enough and is considerably less expensive.
Here's essentially how the track bar moves the axle to the side as the suspension height increase. Look at the letter Z. The bottom of the Z represents the axle, the top line represents the frame. The horizontal line is the track bar and it serves to center the axle left-to-right under the Jeep. Lifting the top line, the frame, via a suspension lift, will as you can see pull the lower line (axle) over.
This photo of the front suspension shows the track bar. Note the track bar in the photo is actually that of an aftermarket trackbar with an adjustment sleeve on its left side used to adjust its length. The factory track bar length has a fixed length without the adjustment sleeve shown below. The sleeve is the short length with bolts at both ends to lock its adjustment in place.
Also note the Pitman arm, leave the factory Pitman arm as mentioned above. Hope this helped a bit.
