I have a 2016 silverado with the 5.3, this is what i have done so far, and i hope it helps you.
-At 1k miles i changed my oil filter.
-At 2500 miles i changed my oil (i know this isnt scientific or anything but the oil was VERY black) and filter.
-At 5000 miles i changed my oil (more of a dark amber this time, not so dark...) and filter and also i looked at my throttle body (which actually needed cleaned, surprisingly...).
-At 8000 miles i changed my oil (less dark than before, looked good) and filter, front and rear differential fluid (front differential fluid looked like brown watery grease... no idea why? rear differential has shimmery with metal flakes and very dark), fully changed my transmission fluid (was still red, had a shimmer on the top of the fluid i had extracted), changed my transfer case fluid (looked good, still red, slight shimmer on top of the fluid i extracted), and also added a PCV catch can.
I am now at 10k miles or maybe a hair less, and i have already caught oil (about enough to fill up one of those little paper bathroom cups) and what seems to be unburnt fuel (smells like it anyhow).
This is what i have done and my findings, YMMV, but i hope this helps you in some form or fashion.
To save the possible crucifixion from other members, I did it because i wanted to, not because it NEEDED to be done.
Just a peace of mind thing for me.
Add: I also have ran a tank of MMO every 3000 miles or so to keep injectors and fuel system clean and to keep it from forming any sort of deposits. And i have also injected water into my PCV return line (from PVC catch can to engine intake) as a preventative measure to hopefully keep valve deposits to a minimum.
(insert flame suit)