You've really got a lot to read about. I'd highly suggest reading the Technical Manuals for the HMMWV (TMs). You can find most of them here
http://www.steelsoldiers.com/forumdisplay.php?119-Present-Conflict-Vehicles-TMs
Reading the Operator's Manual is going to be a must. It has maintenance intervals for when you should be completing various tasks, plus it tells you the various inspections you should do every time you go to operate the vehicle, what to observe as you operate, and post-operation tasks. If you want your HMMWV to run, run for a long time, and most importantly-not cause harm to you or someone else by literally having a wheel fall off or your vehicle catch fire, read it and follow the instructions. The unit maintenance and direct support maintenance manuals will tell you how to complete the tasks the operator's manual states must be completed.
For a new-to-me HMMWV that has an unknown maintenance history, I would consider these items mandatory service before going for your first drive in it: new engine oil and filter; clean air filter; new fuel filter element; inspect transmission fluid; inspect transfer case fluid; inspect/replace geared hub seals; replace geared hub oil; properly set spindle nuts with new spider lockwashers; inspect coolant level; inspect power steering fluid; inspect brake fluid; inspect all calipers and rotors; inspect all suspension components for cracks, excessive play, or loose fittings (check the torque with a torque wrench!); clean, inspect, tighten, and protect all major electrical connections (battery box, starter, alternator, engine harness) in order to avoid expensive electrical failure due to poor or loose connections-bad ground WILL destroy your expensive PCB/EESS/S3 box instantly; check battery fluid levels and top with distilled water only as necessary; charge and load test both batteries separately; and inspect your engine mounts. If you see any seal that's cracked or leaking, you'll need to replace it. I'm sure my list is not comprehensive, but the TM will be. If you want to see a list that Kascar put together (and to help make it obvious what kind of maintenance intervals you're looking at on a HMMWV), check this out:
https://real4wd.com/maintenance/ At the very bottom, you'll see the breakdown of what maintenace group A, B, and C is. Do note that their list was written for a Hummer H1, which will be just a bit different than your HMMWV. Just to say it one last time, read the TMs-you'll be a sick HMMWV owner and operator and every one of your peers here will love you for it.
As for the 4 speed transmission, it will help you get a little bit faster, but I wouldn't recommend it for that purpose. It's really best for helping bring down your engine RPM during sustained highway use of 55-60 MPH operation. If you try and run your HMMWV at or over 70 MPH for anything longer than a couple minute sprint, you're very likely to harm the engine, as it will be running at very high RPM for that engine. You have to remember that the transfer case gears down the transmission's output, and then the geared hubs ALSO gear down that output even farther, which is what makes this truck that much slower than similar vehicles, but helps it be better off road. If you wanted to install one, prepare to spend ludicrous amounts of money or prepare to spend a significant amount of money and a whole lot of hours of your life under the HMMWV. Switching to the 4L80E transmission involves adding numerous sensors, switches, relays, a transmission computer, and a new wiring harness to your HMMWV in order to operate it. This is because the 4L80E is electronically controlled and the 3L80 was mechanically controlled.
I can't really speak about a turbocharger install, except that it requries a new exhaust, a different fuel injection pump, the turbocharger itself, and various other small components. I don't often see all the components for sale for any reasonable price. Most peoople that "install" a turbocharger actually just buy a complete, new driveline (engine, transmission, transfercase) that already has the turbocharger installed from the factory from a scrapyard, such as Southern Metals in South Carolina. It's still a very big job to take on.
As for that "A1" at the end, that's referring to the model revision. As far as I know, you have the original HMMWVs, the A1 series, and A2 series (which mostly had different model numbers), the ECV HMMWVs, and the REV HMMWVs. Each new version is just a collection of improvements made to the past model, built-in when originally delivered. The A1 is great balance of cost and performance, as it has an upgraded driveline with a stronger transfer case, propeller shafts (driveshafts), and CV axles (half shafts). There are also several other improvements made, but I really couldn't list them all... The A2 series' biggest improvement is having the 4L80E installed, standard, and a stronger frame. The ECV greatly improves the suspension and I believe universally has the turbodiesel-it was built to be uparmored or carry heavy shelters. I also believe it added improvements to the cooling stack. The REV has improvement that I'm the least familiar with. I know it switched to helical cut gears in the hubs (like the 2006 H1 Alpha), added stronger Wilwood brakes, and used a different spindle lock nut.
