Reading this thread is like sifting through corn-laden turds looking for a nugget of gold. Let's sort the wheat from the chaff.
First of all, if you start with a Rubicon you've got a good base. There are pros and cons of the 3.6L Pentastar (2012+) vs the 3.8L (2007-2011). Certainly the newer engine will perform better but it also costs more, and the 3.6L is infamous for bad heads (repair of which would not be covered under warranty unless you buy from a Jeep dealer that provides such a warranty).
You can fit 35's under a Rubicon with zero lift, flat fenders (or significantly trimmed stock fender flares) and correct bumpstops. Unfortunately, once you add weight (steel bumpers, winch) the stock springs will sag. But TC is correct that 2.5" lift is sufficient for 35's with either extended bumpstops or minor trimming of the stock fenders, and 2.5" lift will also help with the breakover angle of the longer Unlimited.
I have nothing against AEV lifts except that they rely on drop brackets to correct the front geometry. This works very well on-pavement in avoiding camber-related alignment problems, and so short of going with a long arm lift, AEV results in the best on-road manners. Unfortunately, off-road the drop brackets hang low and get caught-up and bashed on obstacles. For light wheeling the AEV kit is fine, but if you will encounter any big rocks, downed trees or ledges the drop brackets will be a liability.
I've helped more than half a dozen people install Rock Krawler 2.5-3.5" lifts and, aside from some concerns about their rod ends, they perform well on both the street and off-road. If you want something beefier, Clayton and Synergy use Johnnie Joints, which are, IMHO, the most durable rod end you can use. Sticking with 2.5" on an Unlimited will help forestall problems with the OEM drive shafts and the need to do a flipped drag link to avoid bump steer.
The kit you select should have all eight adjustable control arms, new rear swaybar links, new front quick-disconnect swaybar links, progressive springs of the desired length, shocks to match the springs (I suggest spending extra for rebuildable shocks, preferably with remote reservoirs), beefy front track bar and steering stabilizer relocation bracket, adjustable front track bar, beefy rear track bar relocation bracket, extended front quick-disconnect swaybar links and extended rear fixed swaybar links, and brake line relocation brackets. If you can't afford to get a kit with all eight control arms, the minimum needed to set camber and pinion angle are the four upper control arms, but this will mean your axles will be slightly pushed forward/back and you are left with flimsy rear lower control arms.
In addition to the lift kit, to fit 35's you will need new wheels with 4.5" or less backspacing or 1.5" wheel spacers for your stock wheels, and you will need to trim the stock Rubicon rock rail and trim or bend in the pinch seam in your rear wheel wells.
The Rubicon comes with rock rails that will be perfectly fine for protecting your rockers during occasional light to moderate off-roading (see note above about trimming for 35's) and a skid for your transfer case. However the Rubi lacks any protection for the engine oil pan or lower control arm mounts, and provides only partial protection for the transmission oil pan. If you will be wheeling over rocks or downed trees you will want to add skid plates for the oil pan and lower control arm mounts, and consider upgrading your transmission skids. Also, if you wind up with a 2011 or earlier you will want to either relocate or put a skid on the plastic evap canister located next to the rear driveshaft towards the back of the floor pan.
Some other things you might consider, as they are frequent concerns off-roading, is reinforcing your front axle with C-Gussets and either an inner axle sleeve or axle truss. In fact, if it is within your budget or skills allow, (due to lengthy and involved welding process), I would suggest the Artec axle armor kit. And also consider installing the Synergy sector shaft and upper track bar reinforcement kit to address these two additional weak areas.
If you're buying a JK equipped with an automatic transmission I'd suggest an auxiliary transmission oil cooler. And an auxiliary oil cooler for the power steering is also a very good idea (or always carry some extra power steering fluid when off-roading). Then, if you expect to encounter water deeper than your frame, you will want to extend your axle, transmission and transfer case breather hoses to prevent water infiltration into those components.
The stock JK headlights are abysmal, but you don't need to spend $450 on headlights to get significant improvement. A good set of H4 headlight lamps and bulbs with a replacement wiring harness will run you under $200. Spend the other $250 on a small LED light bar for use when you're off-roading.