I also recommend sticking with good quality "OEM style" (paper media) air filters. They provide the best filtration. I haven't compared "brands" on these yet (for the H3) so can't comment on which brand for the H3 is a good option but I've used purolator/wix/fram in the past on other vehicles without issues. I make a point to see which brand is building the best looking filter for the application and go with it. Yes, sometimes that is a FRAM, despite their bad reputation from a bygone era. (though these days, FRAM is building some of the finest oil and air filters available so take a closer look!). I like to look for more pleats, more structure/rigidity (cross members where required), thicker/better feeling seals, etc. This will vary from application to application. If you are trying to get more power out of the engine, go ahead and go with a K&N or similar reduced-filtration, high flow media solution.
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For diff fluids, any modern 75W90 GL-5 synthetic is going to be fine. If you intend to tow a lot or do a lot of hard wheeling, consider 75W140 synthetic instead. In either case, there is no meaningful difference between brands on the shelf of local stores, so just get what you can find cheap. Store brands are fine here. If you want to go for something "fancy," order some RedLine Heavy ShockProof. 75W-90 will be a bit better on fuel economy and getting power to the road, while 75W-140 will buy a bit more wear protection.
For transmission fluid assuming the automatic transmission, any Dex VI or Dex III conforming ATF should work fine. If you want to go a little fancy for not much more money, valvoline maxlife full syn ATF is good and cheap. If you want to go fancy, redline D4 or D6 are worth a look. IMO I'd go with D4 if you want a bit more protection (slightly higher viscosity), and D6 if you want to eek out fuel economy/power.
For T-case, calls for DEX III or DEX VI or a special GM part number depending on what year your manual was printed. There's a ton of debate about which fluid is correct for these but the debate is probably silly because the answer is that all the fluids specified for this transfer case are likely to work fine. Dex III, Dex VI, special GM part numbers used to obfuscate, whatever you want. If you want to truly "upgrade" from the specified fluid, I'd look seriously at Redline High-Temp ATF, which is thicker and better suited for the forces involved that far down the driveline IMO. I intend to switch to this sometime down the road to provide a bit of protection for the additional heat anticipated from adding skid plates. If you want to maximize fuel economy and power to the road, go with a Dex VI product. If you want to maximize gear/chain protection, consider the Redline High Temp ATF stuff.
As for the transmission, T-Case, and diffs, it's likely that none have had their fluids changed, so it may be wise to plan on using cheap fluid in there on a shorter interval as a sort of cleaning flush.
As for engine oil, any 5W-30, 0W-30, 0W-40 API SN or better will work fine. A 5w-40 HDEO is also an option. I personally prefer to use various HDEO synthetics in all my vehicle engines. Lately I pick up whatever ACEA A3/B4 0W-30 or 0W-40 I can get cheapest. Walmart sells several options meeting the A3/B4 spec in 5 qt jugs for the same price as other synthetics. If you're going to run synthetic anyway (which most people do these days anyway), you may as well get one with better cold flow performance, better high HTHS viscosity, and better barrier lube add packs for the same price. This stuff is specified for use in turbo gas/diesel engines and most performance engines in european cars and sort of falls in-between what you'd get from a mainstream 5W-30 and a "heavy duty" HDEO like Rotella T6 5W-40. T6 is also great oil and would probably work great in the abused little i5, but T6 does run on the thicker end of a 40 weight, while most A3/B4 oils run on the thick end of a 30 weight or thin end of a 40 weight, while having better cold flow properties, so should strike a good balance for fuel economy and engine protection. That being said, my old isuzu always seemed to work best on T6. Ran quietest on it, seemed to have the best power on it, burned the least amount of oil on it and also didn't leak a drop when that was in the crank. All other oils seemed to leak and burn faster in that engine while running noisier. If you want to maximize engine protection, consider an HDEO like T6 or pretty much any 5W-40 synthetic meeting API CJ-4 / ACEA E9 performance category specification. If you want to maximize fuel economy and power, pick a 0W30 leaning to the thin end of 30 weight with a lower HTHS and non-HDEO characteristics, like Mobile 1 0W-30 Advanced Fuel Economy.
It would make sense to me, to be consistent with your approach to to bottom on choice of drivetrain fluids and air filtration. Pick if you want to lean on the side of caution, with thicker lubrication providing better boundary protection and reduced wear and more restrictive air and oil filters robbing power, or lean on the side of fuel economy and power output with high flow, non paper media air filters and thinner oils top to bottom.
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Don't forget the BRAKE FLUID!! this stuff should be changed every 2-4 years depending on climate regardless of mileage in most vehicles, and often goes neglected. A full brake fluid flush every few years will protect the metal guts of your brake system from rust damage. DOT 3/4 BRAKE fluid is hygroscopic!
I think valvoline DOT 3/4 fluid is a great value as it often goes on sale buy one get one at advance auto. With this fluid, the frequency that it is changed is more important than the brand name on the bottle by a long shot. It's all the same stuff. I advise DOT 4 for better high heat tolerance if you do a lot of hard braking or trailering. Otherwise DOT 3 is fine and is technically a bit less hygroscopic so shouldn't need to be changed as often so either way. I'm running 35's on mine so opted for DOT 4. Do not use DOT 5, it is not compatible with the system.
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Power Steering Fluid: GM, like almost all makes, likes to really try to obfuscate the crap out of fluids with "part numbers," to get people to buy their expensive bottle of cheap fluid. Based on the research I have done, the various part numbers you might run into in an H3 manual for power steering fluid all pretty much mean the same thing: "basic power steering fluid." Just pick up a bottle of power steering fluid. I like to make a point to suck the reservoir dry and refill with fresh fluid, then cycle the steering and repeat that a few times until it is running pretty clean looking, then redo that once every couple years.
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Oh yea... and one last thing. Don't forget the snake oil!!! lol.... In all honestly, you should never need to put an additive in any hole of any modern car, however, if you feel compelled to put more than just the usual stuff in a hole, here's some ideas that I happen to like:
For your engine, transmission, t-case, diffs, and power steering, Auto-RX is a gentle metal cleaner made from ester oils that you can leave in these systems long term to remove varnish and some other deposits in areas where there is high oil flow. I'm a believer in this product because I have seen it clean things up, reduce oil consumption and leaking on some engines and power steering systems. I also recall after having run it in a transmission that was opened up for a rebuild (not a required rebuild, just had it out anyway because I was having a married t-case upgraded to lower gearing). I asked the rebuilder about how the transmission looked and if it was worth opening up after the fact. He advised replacing the syncro friction cones and a couple forks that were wore out from age, but also commented on how unusually clean the inside of the unit was. Said he'd never seen a transmission at that age (~180K miles at the time) that looked so clean inside. He said the mating surfaces of the gears and all the shafts and everything were just unusually shiny/clean, like brand new metal with no varnish/deposits. The premise of the Auto-RX concept is that oil works best at protecting clean metal. Oil is actually repelled from varnished surfaces to an extent, preventing proper lubrication. The product actually has a neat story behind its invention (not car related, not "snake oil/as-seen-on-tv" origins), and a history of industrial use in commercial applications with proven results. I'll probably do a bit of ARX in hummer holes someday for good measure.
For top-end cleaning, (removing carbon deposits), water or methanol sucked down the intake do work. Products like Seafoam are also fun for this as they smoke out the whole village! (rolling seafoam?). The cloud of smoke is worth the $8 asking price when fire bans prevent the purchase of smoke bomb fireworks in the summer.
For fuel additives. I can't say with any certainty if a fuel additive has ever made any difference in any car I have owned over the years, but I tend to poor a bottle in the tank of each car at least once every year or 2 because it makes me feel good to poor a fancy bottle of weird looking elixir into the tank and then pretend I'm "fixing" my car as I drive it... lol. Gumout Regane, Chevron Techron, and Redline SI-1, are actually somewhat respected among people who give a darn about what snake oils are snake poop and what snake oils are actually capable of doing something.