JK is a pretty tight design, lots of old issues got solved. OTOH, lots of new ones came to the fore. Let's skip the wimpy engine. Biggest issues resolve around the front axle and front driveshaft. Lift a JK beyond 2" and you have to replace both driveshafts on the 2dr, the front at least on the 4dr. Next comes the front axle. The tubes and inner "C"s are weak like a TJ, but they bend worse because of the JK's added weight. Sleeving (or, re-tubing) & gusseting the axle is the common fix. Add to that the pinion / caster angle conundrum. JKs have a high pinion front axle, but lift beyond 2.5" and front driveline vibes become a maddening issue to solve. Some guys claim they can find a sweet spot using adjustable control arms, with a 4" TF lift & 4 adjustable front arms I tried every setting and never could get what I called an acceptable compromise between handling & DL vibes. I finally installed manual hubs, done. $$$$$$$$!!!!!
Other guys either get a new housing from Dynatrac, et al, or have Poly re-tube & reset the original. If you let the front DL vibes go we have plenty of reports of the transfer cases exploding or shearing off the trans, usually at highway speeds. No SYE issues with JK, and you can get 35s on one with some very simple mods, even just new flares in some cases. You generally need to add spacers to the stock wheels to run larger tires, you need about 4 - 4.5" of backspacing vs the factory wheels 6". Also, just plan on re-gearing from the get go. The factory gear ratios are awful. Also, the factory ball joints are total junk, so plan on replacing them soon after any big tire goes on there.
I did as you plan to do. I scored one and spent a month of research on issues, planning out the build, etc. I did one plan with 37s, another with 35s, in both cases planning on a full 8 arm suspension. On paper I thought I could do a 3" w/35s, save the money and retain the factory 4.10 gears...WRONG!!! If I had to re-gear I figured just go 37s and be done with it. That's what I should have done. I ended up having to re-gear and then went 4" and 37s. Cost me a bundle for going too conservative. The big bugaboo for me was the front axle issues. I had already sleeved, gusseted and Pro Steer ball jointed my stock D44. I didn't want to write all that off and go Pro Rock so I went with Spyntec hubs instead. They are great, but cost a lot to convert the rig. You ned new front & rear axle shafts, and new 5x5.5" wheels to pull this off.