As far as rust prevention checks you didn't mention whether you have a WBH (without body hardware- lower cladding) or cladded AV.......Those with older model fully cladded AVs are starting to find rusted metal under the plastic cladding so if you have that version you may want to remove the plastic and look behind it to catch the rust before it gets bigger. If you do that you will probably need to look at other threads that show how to do that and where to cheaply buy those plastic clips that hold the panels on too since they tend to break when you remove the panels. Another place where some members find rust in behind the rear wheel well, you can remove the tail light assembly to look down to see the mud and gravel accumulated in that area.
If I remember there was multiple gear ratios available to the Z71 AV back in 2003 so you may want to look at the glovebox RPO code sheet to see which ratio your Av came with before you make a change.
You have to realize that the AV is a 6,000 truck with the aerodynamics of a brick so it's not a gas economy vehicle.
The best things you can do to get it's best gas economy is to drive it like an old geezer and be very easy on the gas pedal and brakes, avoid stop and go driving as well as long periods of idling, don't add a lift kit (it gets it up into the airstream and makes more drag), and keep the tires properly inflated and don't get larger/wider tires. The best mileage will be on interstates if speeds are kept near the speed limit,above that you may start to loose mileage. You should expect around 13 miles per gallon in town and close to 20 miles per gallon maybe on the highway. It may vary at times due to your driving style and even outside temps and gas ratings/mixtures can have some effect. (how much ethanol content or winter gas vs. summer gas etc.)
Another thing you may want to consider is replacing the first generation AV front brakes to the second generation brakes. There is a thread covering the GMT 900 Brake swap in the brakes section that has photos and part numbers to get the improved brakes. If you had a stock AV the new brakes don't fit the 16 stock rims but with a Z71 you should have 17" rims so they should fit.
If you plan to put very little mileage on your AV and it will be sitting still for a long time you may want to consider installing an on board battery charger system like they put on boats so you can run an extension cord to keep your AV fully charged. You may also want to rethink your method of starting and having short drives in your AV. The latest thoughts on vehicle storage say if you can't drive it for half an hour or more to totally burn off all internal moisture then you just don't start a motor since the internal moisture will remain in short startups and create internal rusting and acids to form which will contaminate things.