Anyone who can legally own a firearm can make a NFA firearm if they file the proper paperwork. (The exception are machine guns, which cannot be legally made for civilian use.) The paperwork is a Form 1 to make and register a firearm. Who would want to make a NFA firearm? Anyone who wishes to put a short barrel on their AR or shorten the barrel on a shotgun. You can of course make your own silencer, but this is much more technically difficult.
A Form 1 has a similar wait time to a Form 4. However, if you are converting a Title I firearm to a Title II firearm, you can continue to possess and use the Title I firearm while waiting for the return of your paperwork. For some people, this is a necessity.
Should you decide to go the Form 1 route, you must have the firearm engraved prior to converting it to a NFA firearm. The engraving should include the name of the manufacturer, i.e. the person or entity the firearm will be registered to, the city and state of the manufacturer, the caliber or gauge of the firearm, and the make and model of the firearm. All of this must be engraved a minimum depth of .003 inches into the firearm.
If you are converting a firearm, the make, model, and caliber or gauge will already be engraved in the firearm. Thus you will only need to engrave the manufacturer’s name, city, and state.
When manufacturing a firearm in a Trust, the Trust’s full name should be engraved on the firearm. If manufacturing personally, then your name is engraved on the firearm.
Any good engraver can engrave your firearm, but it is best to go through a NFA dealer because this is a registered firearm. Additionally, the engraving must meet a certain level of visibility, and NFA dealers who commonly handle these items know where to engrave each type of firearm.