Should be able to find a used 2012+ rubicon around that price range, but there are certain years that have inherent problems. With the rubicon you'll get 3.73 gears with the auto or 4.10's with the manual, I've had both, the manual was nicer for towing but the shifting got old pretty quick when in town. I pull around my jumping jack trailer, loaded it's roughly 15-1700 lbs, the auto does alright with it, I take it through the mountains and it does it just fine. But that being said you could probably pick up a well optioned sahara for cheaper than the rubicon and spend some money re-gearing and on lockers or limited slips depending on your plans for wheeling.
Problems for model years that I'm aware and some I've experienced first hand are:
2012/13: Known cylinder head issues in the first years of the 3.6, usually starts as a tick but turns into replacing the head.
Transmission programming issues in the rubicons for autos, related to the transmission getting stuck in second when going from low range to hi range, pretty sure their is a program update you can get at the dealer now, or you just put the vehicle back into low, manually shift to 1st gear than shift back to high. Its not a show stopper but a pain in the butt.
2014/15: Oil cooler on the engine known to leak.
Rads are known to leak at the plastic tanks.
Also their are a run of cam position sensor's that are known to be faulty, I have the TSB somewhere and i'll try to post that up later, has the part serial number that stamped on the sensor, easy fix, just replace them and done, usually a symptom is hard starting with the occasional check engine light and torque derate light, goes away on vehicle restart.
All rubicons have the possibility of having the electronic locking sway bar fail, I've had this happen on my 14, was interesting to drive for a week while waiting for the parts.
Ive had a 2012 Auto, 2014 Manual and now a 18JK Auto, I hated my 12 for all the little problems I had with it, my 14 was great for the most part but was tired of shifting, my 18 RECON has been great so far with 40,000km on it. All of them have had all the bells and whistles. I went 18 JK instead of JL because Jeep finally got all the bugs worked out for 17/18, don't hear of many issues with the last 2 years.