What do you like? tinkering, modern technology, nostalgia, car shows, classics, performance, V8 rumpity rump, something to give you a reason to hit swap meets for?
I will only assume you are looking at vehicles with 'modern' conveniences (good sealing tops, AC available, power steering and brakes)
There are pro and cons for virtually every vehicle made.
YJs, and CJs for that matter, are leaf sprung, light, could be had with carburetors if EFI isn't your thing. CJs just draw people to them like a magnet. For 10K you can get a very nice CJ or YJ. You can even get CJs with factory V6s or V8s and they came in Short (CJ5) Medium (CJ6 and CJ7) and Long (CJ8 aka Scramblers). Full cab or 1/2 cab pickups in addition to soft tops! But avoid early YJs with 5 speed peugeot transmissions at all costs. Later YJs got the 4.0L I-6 with EFI. The 4 cyl YJs (and TJs) with the AX-5 5 speeds are known for transmission issues with higher mileage.
TJs got coils springs To me personally the on road ride wasn't enough of an 'improvement' to sway me to them. Offroad however they have better articulation. The EFI'd 4.0 6 cyl is the way to go in this one as it gets you the AX15 5 speed or later a good 6 speed manual option. The interior appointments and comfort/quietness on these is light years better than the previous generations especially when both are compared when running soft tops. Plus the rust protection of the bodies is supposed to have been greatly improved (Not sure how true this is or if folks were just comparing them to CJs that were already 10+ years old when they came out as most tried to overlook the YJs at the time due to their square lights.
I confess I hate electronics that determine if my vehicles run or not, however if I were buying something that I had to trust its easiness so my wife could use it ANYTIME, I'd get a TJ. They have minimal electronics (essentially an engine operating unit and an ABS system if you get a manual trans). The 4.0 has renowned reliability and longevity as well as decent power. $10K would net you a pretty nice TJ. Around me $10K wouldn't even get you close to a 'nice' LJ so that would be totally out. The Rubicon versions just add better axles with locking differentials and lower gearing and a lower geared transfercase. Generally not considered worth the upcharge unless more technical offroading is your thing.
I have owned all but the LJ.
If hardcore offroading isn't a priority (I know its a sacrilege) but I too would suggest checking out the small Suzukis. Samurais (not the best engine reliability over 150K miles) and Trackers are both very light, small, nimble, fun runabouts. Your budget would get you into a pristine example of either and the Sammys have a near cult-like following and their aftermarket is great. Fuel consumption isn't a concern with this type of vehicle decision but it is enough of an advantage with the Zuks to give you an arguing point with a hesitant 'banker'.
I currently live in the convertible capital of the universe and by its very nature there are LOTS of small 4x4s here with soft tops (not everyone wants a new Mustang convertible!). If TJs are like belly-buttons, then JKs are like hair. Nearly EVERY third car is one or the other and unless it is very radical, no one gives them a second glance. A clean CJ or Samurai stock or lightly modded will turn heads (I'm not talking about Uncle Walts camp beater, I mean something that has been taken care of), and a Tracker in nice shape with a little lift and some offroad tires, well you tell me when is the last time you saw one and if you'd take notice? YJs still don't get much respect, but if you find a really nice one at a good deal you can just bolt on a CJ front clip!