I would recommend running Starsan through your system and out the faucets. This way you are also sanitizing the beer lines. This is what you would do when you clean your lines too...run a line cleaner, run water to rinse the cleaner, then run a sanitizer through.
I usually soak all my keg parts in a cleaner and then soak in sanitizer too then the keg back together too. You did not mention sanitizing those parts (ball locks/pin locks disassembled, o-rings taken off everything, etc). Then should all be sanitized too.
Member of the Metro South Homebrew League (Mash-Holes)
Primary - Belgian Pale Ale
Secondary - Empty
Barrel Aging - Empty
Kegged - El Hefe 2.0