Mine have a covered run, but I plan to fence adjacent paddocks. I bought 5-ft. welded wire for that but plan to extend above that with deer and/or poultry netting. I probably will run a couple of strands of electric around the base of that. I figure I'll need to experiment and adjust. Someone on BYC posted a great idea for creating very tall "invisible" fences for relatively low cost, by fastening a second post to one set into the ground to gain extra height, and then hooking netting on simple hooks at the tops of the second posts. Not sure of the materials but I hope to do something similar, but more substantial closer to earth.
I think the right height depends on your specific situation, the breed of chickens you have (how flighty), whether you clip wings, how catastrophic would be an escape, etc. I have a couple of wild-type Easter Eggers who can easily pop up 6 ft. I'd like to add more flighty laying birds but not sure how to keep them in, as have trees and roofs also accessible.