I have a 99 suburban and it's a super reliable workhorse. It's got 250k on the clock and until recently it's been trouble free. Just basic maintenance..The issue with the Tahoe is the space behind the rear seat, There isn't any if someone is sitting in the back row. Sure you can put a couple of small bags back there but if you have a bunch of kids or a dog kennel to travel with there just isn't enough room. My knowledge of the 5.3's after 2000 is limited.
2 weeks ago I drove my daughter-in-law and 3 grand kids and dog from Norfolk to ATL in their Expedition. Same issue as a tahoe. It's just to small for big families. Get the Suburban or extended Expedition/Navigator.
Also, there were some issues with the 5.4's in the fords around that year range your looking at. Cam phazers failing.