Searching has already yielded a lot of great results so far! I wish the previous owner had found this site and put some effort into the truck, but then again, I would not have been able to get it for a good deal.
Here's my to do list. Please let me know if there is something I am NOT already finding that I should inspect before it bites me.

ENGINE
rough idle - Clean Throttle body, clean MAF, tighten intake bolts.
pull one spark plug and see if they are OEM or not. What are the OEM parts, AC Delco? And check for water around C.O.P.
Tighten valve cover as I see some oil around its edges
Cam position sensor, pull out and clean. I think it is on the front of the engine. Seems almost too easy to get too.
There is a grill mounted air inlet tube on the passenger side that looks like it serves to bring in cool air to the battery. but it just flops around. I want to zip tie it down or delete it. Ideas?

SUSPENSION:
Front end is too low. The bump stop material is gone and the control arm is about 2" away from hitting the metal of the bump stop! the plan is a DIY lift with new longer shocks. Going to time that with new tires.
Rear seems to be ok. Simplicity of Leaf springs.

DRIVETRAIN:
There seems to be more noise than should be coming from the front. Not sure if it is a bushing vibration noise or not. I don't feel anything. Just noise like a clutch fan stuck. When I change the oil I am going to inspect all of that area before changing diff' fluid and checking out the gears inside.

BODY
Sunroof has leaked before. Need to check the drain lines.
Rear tail gate cabin vent has no seal and is flopping around. Still trying to decide if I want to delete the spare tire and bracket and doing the Big Rig light show that HummerZ did. Considering putting the tire up top on a roof rack.
side mirrors do not fold in. I'm talking 30+ pounds of force and they don't budge! Any tips for getting these unstock so I can rotate, or should I just leave sleeping dogs lie and move on.
side mirrors shake while going down the road. Talk about a failed design. The mirrors on my 1971 Chevelle are fairing better. LOL

ELECTRICAL
Drive's door lock is sticking or weak to move when it is actuated electrically. Moves just find with my finger.
Gas gauge I think works. bought it at half tank and drove it down to 1/4 tank.
A few exterior lights are out (side marker, license plate)


Anything else major I should start to watch out for?

 

Is yours a RH-drive model? My battery cool air tube is on the driver's side. The battery end pushes onto a collar on the case, and the grille end uses a common push-in body clip - work around as needed/wanted.

When were all of the fluids last changed?

 

Doh! Sorry. Tube is Driver's side. Mail truck H3 would be awesome though.
So my body clips part is missing for that tube. Good to know that it should point at the tube.

No clue on maintenance history. I plan to do all fluids and filters.

 

Hmmm, i cannot find an edit feature for my posts. Always something challenging in life. LOL

 

Full features show up after you make enough posts, like 10-20 or whatever.

 

Longer shocks will do nothing to raise the front end. Shocks "smooth out" the ride, springs (in this case, the torsion arms) support the ride. Just tighten up the torsion arms (do a search on this site). You want 23.5" from fender lip to center of hub. Any further than that will start to cause problems with CV joints.

 

H3 Front Bump Stops are pretty cheap and easy to install. New Genuine GM 15783030 2006-2010 HUMMER H3 H3T Front Suspension Jounce Bumper

 

650Hawk. True. I get how Torsion bars work. I left out the part about turning a breaker bar with the 1-1/4" socket on it. I could see how my short sentence should have been worded different.

Thanks for the link on the bump stops.

Got some new battery cable wire end terminals put on, and in the process deleted the On-star after thought power lead.

The front differential bushing are all in need of replacing.

I have a new item to add to the list.... I think it's a head gasket. new thread on that here:
https://www.hummerforums.com/forum/h...t-steps-48601/

Everything else is on hold until I make sure this truck is worth more effort and doesn't nickel and dime me to death.

 

So with a 19 year old H3. its a journey to keep it up to snuf...

Prioritize what to do so you skip the small stuff.

Be methodical and take your time.