The guiding principle should be that the actual vehicle isn't so critical if you're not circumnavigating the globe with it. Most places in Utah you are within walking distance of not dying. My first wheeling experiences were in my buddy's '85 Cherokee he picked up for a few hundred bucks, welded the rear diff, did the hockey puck lift, and we tackled most of the trails at Moab. I would pick a vehicle that has a strong following so that parts and repair tips are plentiful. My picks:
Jeep Cherokee XJ ('97-01): Pros - Ch$$p, strong, proven drivetrain, light, capable, plentiful, solid axles, lots of aftermarket support. Ch$$$$$$p. Cons - Old, no proper frame. "Tin can" feeling.
Jeep Wrangler (newest with light mods that budget allows): Pros - made for trails, gazillion parts, easy bolt-on mods, plenty of enthusiasts, top/doors come off. Rubicon package FTW: stronger axles, F/R lockers, lower gear ratio, etc. Cons - can be expensive to get into, Chrysler build quality...
Toyota Tacoma ('99-04, TRD package) Pros - Light, bulletproof, small size allows for narrow trail access, cargo capacity (shell, sleep in back?), multi-use vehicle (haul bikes, etc), plenty of enthusiasts, capable off road. High re-sell. Cons - High re-sell means high purchase price, aka Tacoma Tax. Quite ridiculous, actually. Way overvalued on the used market, but hey...still awesome.
Toyota 4Runner ('95-02) Pros - Toyota quality, small size, wagon configuration (sleep inside), factory rear locker available. Cons - Not as capable as jeeps, not as versatile as tacomas. Compromise vehicle.
Toyota Land Cruiser/Lexus LX450 ('94-97) Pros - Very heavy duty build quality, solid axles, lots of aftermarket support, high payload capacity. Better for overland/expedition type use vs wheeling, but can be modified to wheel quite well. Available front and rear factory lockers. Cons - expensive parts, heavy vehicle means 11-13 mpg after mods (before mods?), 17-20 yr old vehicles at this point. Some issues with head gaskets, weak brakes.
Vehicles to avoid:
Anything Land Rover
Anything that has been wildly modified in a buddy's garage while they were inebriated (most stuff in KSL rock crawler section...)
I would avoid niche or orphaned vehicles unless you just have a burning passion to be unique rather than practical (Isuzu, Mitsubishi...Unimog, humvee)
I personally don't go for vintage vehicles (pre mid 90's) unless that is verifiably your "thing" and you know you will love tinkering
Bottom line: Pick something that suits your personality, is in good working order, is a make/model with a decent reputation for reliability and capability, is within budget, and get out and have fun. It's not about the vehicle, its about the outdoor experience.