Congrats on your purchase and welcome to TDS. Lots of helpful folks here, and plenty of useful advice to be found.
Your truck sounds pretty sweet, 79K is barely broken in. There are folks on this forum with 400K+. Keep up with the maintenance, especially coolant changes. Use of Fleetguard DCA4 SCA (supplemental coolant additive) and periodic testing of same is critical to prevent cavitation, which causes pinholes through the cylinder walls from the water jacket.
The C6 is pretty much bulletproof, but not very efficient. Folks with E4OD (auto w/overdrive) and ZF5 (manual) get better mileage, all other factors being equal. The C6 also doesn't have very steep 1st or reverse gears. If you plan to pull heavy loads, I hope you have a 4:10 or numerically higher rear end. I swapped a 3:55 into mine and don't regret it, but I only tow about 5K, and wouldn't want to pull too much more.
If your tranny fluid looks or smells original, change it and the filter screen below the valve body inside the pan. Be prepared to take a bath in ATF :lol: Drain the torque converter too, there's a drain plug in the face accessible through a hole in the flywheel. Also use a blow gun to clean out the cooler and lines. The whole system takes 12 quarts to fill. Add 4 quarts, start and run it a minute, stop and add a couple more, repeat. Avoid overfilling. It will take a while to refill the system. Don't attempt to put it in gear until you've got all 12 quarts in and the level is in the crosshatch on the stick while the truck is idling.
One other common problem is the in-tank fuel pickups, they tend to break when they age. The truck will run out of fuel with about 1/4 tank on the gauge. Keep a jerry can full of fuel (or 1 tank full at all times), a small coffee can, a rag or two, and a 5/8" wrench handy until you know if you have this problem.
If/when you run out of fuel, switch to the full tank or add 5 gallons. Then crank the engine while holding the schrader valve on top of the fuel filter open. Hold the coffee can under the valve to catch the fuel. You'll get lots of air at first, but the filter should fill within two crank cycles. Speaking of which, to avoid starter damage, crank no more than 30 seconds at a time with a 2 minute rest period between cycles.
If the engine doesn't start once you get clear fuel at the schrader, use the 5/8" wrench to crack the line fittings on a couple of injectors, then crank another cycle. This gives air in the IP an easy point to escape. Once the engine starts, close the fittings with it idling and mop up any spillage. There won't be much, there's very little fuel flow at idle. Once you've got it running again, Google "hutch mod" for the in-tank pickup fix.
One last thing, put your truck's specs in your signature. It helps out other members a lot when they're offering help.
