Do you want a coil lift or a budget boost? I'm not a lift expert yet, just a guy that spends way too much time on jk forums. I have been think about adding one myself. Personally I just want to go up to 33" some day. I'm thinking a 2" bb like AEV roughly. I personally don't want more lift in front to level out the factory rake. After 2.25" you need to get an exhaust spacer for a 2dr. That's based off a teraflex YouTube video. 4drs also have the option to use an aEf exhaust y-pipe so the driveline won't hit the exhaust crossover..
Coils give the most flex and advantage offroad. Most if not all 2.5" kits on a coil will likely give you at least 3", or more if your close to stock weight. Too much lift can create issues = $. Most kits will add more lift to the front to level the rake. You can add spacers on the rear coils if you don't want that. Teraflex is often called a firm coil lift. It requires more wheel back spacing on the rear wheels because of the swaybar link. A pair of 1.5" wheel spacers or aftermarket wheels with around 4.5" or less can be used. Your going to need to do that anyways for bigger tires. Rock Krawler gets good reviews but adds LOTS of extra actual lift. Metal Cloak is starting to build up some buzz, but they are pretty new on the block. AEV is supposed to have good road manners at the price of lowering your ground clearance some with the corrective LCA brackets. I would steer clear of Rough Country's coil lifts because they are known to sag.
Somewhere over 3" creates problems with the driveline boot by the cv joints, and will shorten the u-joint, on the front driveline. Cardan u-joints life quickens the more angle it has on it. With autos the stock drivelines middle boot can rub the transmission when under a lot of flex. Over 3" and you start to reach a point where you might want adjustable drag links vs corrective brackets included with most kits. That will help center the axle left to right. Also adjustable lower control arms (or AEVs corrective brackets that lower ground clearance) can be used to correct the caster and extend the wheel base( front to back axle length) that gets shorter the higher you go. To get even fancier you can flip the drag link which honestly I still haven't visualized how that works. Basically a coil lift can be a money spending process to get to what you want. If you don't have a grand that could go towards aftermarket double cardan driveshafts I personally would steer clear. I could be overly cautious though.
Budget Boost (bb)/spacer lifts will give you more of a true actual advertised lift but may sag after adding heavy bumpers, etc. With a 2d you could get a set of 4d coils to help correct the sag perhaps. You look at the 2 last numbers on the spring coils to know how stiff what you have is. There are a good amount of options that are all about the same. Rough Country has a metal 2.5" bb. It's like $140 and gets recommended. There kit does not address the trackbar. They claim at 2.5" lift the axle only shifts a .25" sideways. From reading threads I think it could be up to .5". Teraflex has a super popular very complete 2.5" bb. The have you add a corrective bracket on the track bar mount. It requires drilling a hole. This should take care of centering the axle. If you don't want to drill the hole you could get a rear adjustable trackbar that could be used on a coil lift in the future. With 2012+ JK's you need the exhaust spacer. I don't know why they don't make that more clear in there kit descriptions. The teraflex guy has posted on here it is needed. You can get there kit with longer shocks, buy your own, or shock extensions. It has been recommended to keep the rubicon shocks if you have them with the extensions. I would guess that would limit your flex but would be great on road. The base shocks are crap and should be swapped out. So if you have the money, or down the road what shocks do you want?
The Rancho 9000 are adjustable and get good reviews. The Bilstein 5100 get lots of recommendations. I have also heard that they can be borderline bone jarringly stiff. It seems like I read the teraflex shocks are rebranded Fox shocks. I haven't heard enough to comment on Fox shocks. That's about all the forum info I can regurgitate.
WILL IT RUB
There are a few threads about this if you search.
Here are some basics.
33" will fit without a lift. If you dissconnect the swaybar you will need at least over 3/4". As in it will rub and I don't know the minimum. Most catalogs say 2" lifts are good for 33".
35" will fit with 2.5" of lift. If you dissconnect it might rub. Trimed/bushwaker fenders should be enough to make it work ( I think).