Ideally, a 1 to 1 1/8" ID, heavy wall pipe. I like heavy wall because it's wall thickness allows me to drill/tap 3 holes equally around the OD (I used 5/16"-18 for my smaller forge, and 1/2"-13 threads/bolts on my welding forge)
A little "wiggle room" is nice to have (a 1 1/8" ID pipe) because over time the burner end will become a bit larger to to all the heating/cooling cycles. But you don't want to go too large, otherwise you'll have flames licking out the pipe that holds the burner....and if it's too much, the flame will get pre-ignited inside the burner pipe. There's also nothing wrong with stuffing small pieces of ceramic fiber into any cracks between the burner and the burner holder.