IF you do this, forget the GI type aluminum vise jaws. Get the action block type, a plastic contraption that hinges over the receiver, with a plug to fill the space normally taken by the bolt carrier.
The GI type vise jaws clamp the barrel into a vice. The receiver is put onto the barrel. The barrel nut is torqued. The torque puts pressure against a locating pin pressed into the top of he barrel, which indexes the barrel vertically in a slot in the receiver. So, as you twist the barrel nut, the receiver wants to twist around the barrel. The aluminum is easily dented by the steel pin.
The much better action block clamps around the upper receiver, and mounts into a vise. The barrel is plugged into the receiver. The barrel nut is now torqued against the receiver, which is held steady. The barrel can be mounted straighter. A FAR better way to do it.
Use a regular automotive torque wrench with 1/2" drive, plugged into the 1/2" square hole in the GI barrel wrench. The GI wrench is fine, but there are better wrenches, if you want to spend a little more, with more cutouts for other parts, the flash suppressor, the receiver extension (buffer tube), etc. And these grip more teeth on the barrel nut.
Lube the threads with regular old moly wheel bearing grease. I usually get good gas tube alignment in the 35-50 ft-lb range, but you can go up to the specs in the manual if need be. Higher is not better, just as long as you are over the 31 ft-lb minimum.