Aeroshell 33.
It's what the TM calls for and it is easy enough to find.
You have to be careful with anti seize. As mentioned galvanic corrosion is a possibility. Make sure that whatever you use contains no graphite, that is the key.
MarkCo's technique of torqueing 3 times before your final assembly is spot on but I change it up just a bit.
I will snug up the barrel nut dry. I don't bring it to full torque though, just snug it a few times. I go by feel, you can feel the roughness of the anodizing and snugging it up dry a few times burnishes the threads. You will feel it get smoother the more you do it.
I will use brake cleaner or similar to clean the nut and threads after burnishing them and blow them off dry.
On final assembly use the Aeroshell and they torque up really nice and smooth.
The torque specs in the TM are a huge range, they are 35-80 ft/lbs and they are meant to allow the castleations of the barrel nut to line up with the gas tube.
I like to shoot for 55-60 ft/lbs ideally, if I can't get there I will try a different barrel nut or use barrel nut shims.