I’ll be using wood post but thought I would use metal pipe for the brace.I'm sure fence and others will chime in but 2 inch diameter 1/8 inch wall won't be overkill but it's thick enough.
I personally use 4 1/2" diameter 1/4" wall uprights and 2 3/8" diameter ~7/32" wall brace. I do it as much for longevity as looks.
I had to do a Google search for pipe bullet. Once I got past all the pot smoking paraphernalia I discovered a pretty slick looking way to join pipe lolI drive two eight foot long 2 7/8 pipe three feet into the ground. I connect them horizontally with a 2 3/8 pipe cut to length. If I’m welding them, I’ll saddle cut and join them. If I can’t get a welder to them, i’ll cut with a sawzz-all and join them using a pipe-bullet.