I don't have the experience of a lot of people on this site but for me, 2 weeks in primary and straight into the keg are standard for anything under 1.060. Of course I check FG but 2 weeks at proper temp and it's usually there. So, I basically secondary in my keg for a couple weeks and then serve (or just serve if I'm thirsty).
Same for lagering. Primary, keg and into the fridge for 6 weeks or so. No glass or plastic secondary.
I throw the CO2 on at 20+ lbs to set the keg seals and then hit it once in a while to make sure it has pressure. But, like you guessed, move the keg and you get cloudy beer for a bit again. If I'm taking a keg somewhere, I keg and fine, let sit and re-keg to a fresh one. Otherwise, it stays in the first keg.