I used to own a 95 K1500, 03 Tahoe, 05 Z71 Suburban and currently have a 2000 Silverado. I've had a little experience with full size GM trucks/suv's.
If you live near a Wal-Mart, I would go with Valvoline Max-Life 5w30 and either AC Delco P61 or FRAM TG3675 filters (both are "long" version).
Regular Max-Life is already a Synthetic Blend and the only "High Mileage" oil I would consider using normal OCI's. The full-syn version is of limited availability in my area, if you can get that at a reasonable price, then go with it.
Furthermore, you should look through the paperwork to see if there was any service done to the transfer case.
GM trucks and SUV's from 1999-2007 had an issue known as "transfer case pump rub" where an internal component caused a small crack/hole to occur in the housing of the transfer case and subsequent leak of the fluid only while driving.
This caused failure of the transfer case and possible damage to other parts of the drivetrain from the chain reaction of events.
More information can be found here..
https://www.merchant-automotive.com/p-4017-transfer-case-pump-upgrade-kit.aspx
I am not affiliated with Merchant Automotive, but I think they were the first company to develop and sell a fix for these transfer cases. It seems the problem is "not if, but when" these units will fail. MA is well known in the Duramax/Allison crowd.
If there was no evidence that the transfer case was repaired or serviced with updated parts to prevent the "pump rub", I would buy the kit from MA and install it for preventative maintenance.
You may want to flush the power steering system with Valvoline Maxlife P/S Fluid. I just disconnect the return line and clamp a hose to it to drain to a jug, then refill the system as it pumps it out. Quick and painless.
The 4-wheel drive system on 99-07 GM's sometimes had issues with the "encoder ring" and I think the 4-wheel drive engagement solenoid. Those were the two main culprits when the "Service 4wd Soon" message appears on the instrument cluster.
Good luck with your new purchase.
I wish I never sold my 2005 Suburban Z-71. I had bought it used and it also came with a stack of documented services. I loved that truck!