The trust is pretty simple to do. The best way is to have it set up by a lawyer so that it addresses everything you want it to (in case you have any personal requirements for it), but a quicken trust is cheaper and works just as well (at least as far as getting the weapons registered to the trust).
Because a trust is a separate legal entity, the weapon must be registered to the trust itself (and not you) and therefore the trust is technically the owner, it just allows all trustees to possess and use the weapon. This means that you have to submit another Form 4 and $200 tax to transfer the suppressor from you to the trust. The positive side of you already having it registered in your name is that you can keep the weapon and still use it while you're waiting for the trust's Form 4 to clear (however no one else can possess it outside of your presence before the trust's paperwork comes back).
None of the trustees are required to submit fingerprints, photos, or undergo a background check, but whichever trustee picks up the weapon from the SOT will have to fill out a 4473 just like if you were buying a title 1 firearm.
While the trust is technically the "owner" of the NFA weapons, as grantor you have the ability to amend the trust whenever you like, so that means that you can add or remove other people/trustees as you wish. This is useful in many situations like if you are single and get married, have children you want to be able to possess the weapon, or have a friend who you trust enough to borrow the weapon. Another advantage is that if you have a falling out with a trustee (divorce, etc.) the grantor can also remove the trustee and they will no longer be able to legally possess the weapons. No trustee has "ownership rights" over the items in the trust.