If you want a stock-ish swap, don't hesitate for anything less than 200k, think about it for 250k, and condition matters for 300k. I had a 5.3 in my wife's old suburban with 300k that I pulled out, it was still pristine (except ticking lifters) but had been taken care of. If you don't know the history, stick to 200 and below and you should be fine with basic pulling the valve cover and looking for absolute garbage and other basic info. I did get one with 160k that I didn't look close enough at. If I had, and saw the goopy RTV on the water pump, green coolant, sludge under the valve cover, and a few other signs, I wouldn't have bout it. But for $150, I was already there and he had it ready to set in the bed of the truck, so I grabbed it. My mistake.
If you want to build it up, it depends on what you want. DOD/AFM has crappy failure prone lifters, as mentioned, but if you are going to do a cam swap, it isn't much more to delete it all. I did it in my wife's current Yukon Denali, I think I spent $1300 and gained a fair amount of power. VVT, same thing, not a big deal if you want to swap cams anyway. If you want stock cam, then avoid anything with 3 letters (DOD, AFM, VVT, EPA, FBI, IRS, Etc).
Sloppy Mechanics always preferred the 300k+ engines for turbo builds because the worn rings gives you a little extra cushion, and if you blow it apart with 28 pounds of boost, you don't feel too bad grabbing another short block with 300k and stabbing it in.
If you want a nice driver for your kid and plan on putting 40,000 miles a year on it, yeah, grab yourself a lower mile unit, maybe 100-150k, and make sure it has good oil pressure.
As for accessories, I seem to get around 100k-150k on a water pump and 150-200k on alternators, both are easy swaps and stock parts seem to last longer than even AC Delco replacements. Haven't had a problem with a PS pump failing, although hydroboost hoses will probably need to be replaced. Also transmissions, 200k on a 4L60 and plan on it being toast soon, figure a rebuild. If it has a "fresh" transmission, I'd still consider it garbage unless you know who built it and how. 4L80 should be fine unless you know it has issues, or it was 300k on a cab and chassis or something severe duty like that. But every average half ton and/or suburban is going to have the 4L60, not terrible, but know the limits.