Great! I hope you really like it, I think you will. I love mine, and most of the guys here love theirs! You're going back a few years, might give up a few options, however you're into a totally different type of vehicle. A very capable one. How many miles? What are your DIY or Mechanical capabilities?
Like any vehicle, there are some weaknesses. Lets get them out of the way. These are the initial things I would check if I was buying/receiving a new H3. This doesn't mean there's a ton that goes wrong, but the following are common replacement items:
1) Upper ball joints/Control arms - The ball joints commonly fail. They don't last that long. The lower ball joints seem to hold up pretty well. I would check the uppers first and right awa. The A-arms contain a polished stud pressed into a nylon seat. You have to replace the whole aluminum UCA. But it's pretty easy and inexpensive to replace. The root cause for failure is the grease dries up, or water intrudes (seal fails) ...and either way it happens, the stud becomes dry or rusty and it damages and breaks/wears out the nylon seat. Buy the AC Delco UCA's.
2) Steering rack rubber bushing - There's a rubber liner appx below the driveshaft behinde a bracket that holds the steering rack. Oil gets on the rubber bushing/liner, and/or minor rack movement spits the rubber out. Yours could be worn or even missing. Simple to replace.
3) Front Diff Bushing - Again near the driveshaft on the backside of the front differential is a rubber bushing that has up/down forces on it, and tends to fail. Maybe they went with a more robust system on the H3T's. But on regular H3's that bushing isn't long-lived. You can remove the cross member and replace it. Simple and cheap.
4) Check outer CV joints for up/down movement, esp the driver's side.
5) Check rear output bushing at the transfer case for up/down excessive free-play.
6) Sunroof leaks - This is real common and floods the carpet. Under the carpet GM used the most water-absorbent sponge-like foam that I've ever encountered. It sucks up moisture and doesn't want to let it go. It can make your vehicle smell musty too. There are a lot of threads on it. Essentially, the sunroof seal (if yours has a sunroof), can leak some and excess water is suppose to drain out the front/rear (there are 4x) drain tubes. But a single dead fly and a bunch of other debris can clog up the drain grommets at the firewall. You gotta keep them clean. Your truck could even have 2" of 'mud' at the bottom of the drain tubes (like mine had). Wipe down the sunroof gasket with a wet sponge ..and the seating area on the body. Dirt and muck can built up on the seal after years and reduce it's ability to seal out water. Replacing is actually a really good idea.
7) Battery Connections - H3's like many modern vehicles are really finicky with power and great battery connections are a must. And make sure the grounds are good and seated cleanly. Body and engine. Also, make sure your battery is very good too. When the battery's get weak or bad connections it can do wierd things like flake out the door module (windows and alarms don't work) and it's really frustrating. So if you have any doubt about the battery whatsoever, I would replace it. Save yourself a lot of potential headaches.
8) Passkey/No-start situation - Sometimes people have a no-start situation, due to the alarm. Read in the manual how the alarm works. You may never have a problem (I haven't) but if you go back in time many H3 owners were frustrated up to their ears by the alarm and a no-start situation. I'm not trying to scare you, just prepare you that if your H3 doesn't start sometime, don't freak out. Learn how the alarm is supposed to work. Like I say, it's not super common but just a thing to be aware of, and you will be smarter and wiser for it. The fix for people who have repeated issues seems to be a new key cylinder. But let's not get ahead of ourselves yet.
9) Test Engine - You should probably do a good look-over on it after you get it. I would a) perform a compression test (so you know what you have). Do it warm in accordance to good comp test procedures. b) inspect plugs and replace if needed, c) Same with air filter, d) you'll probably be tempted to put a oil'd cold air kit on it ...the oil from the K&N style filters can goof up MAF sensors (just sayin'). e) Check your truck's oil pressure if it's high miles (these 3.7's seem to be good up to about 190-210k and the chains and bearings give way. f) Verify all sensors are working right, no codes.
10) Replace all fluids - including flushing the power steering system. Unless you know certain things have been changed already.
Note: Parts support from GM is rapidly dwindling. If you have a list of things you need. Best to order them sooner than later.
Well, that's a pretty good start. Welcome. Go and enjoy your new ride!!