First, suppressors are less impressive in person than in the movies. I always laugh when the assassin shoots his target while he's asleep in bed without waking the lady sleeping next to him. No. Suppressors aren't that good.
I haven't seen the movie in question, but I can guess that the gun was a USP Tactical. I can tell you exactly what the process for lawfully owning that gun and suppressor is.
First, you must live in a Class III state. Oregon is. As far as I know, Iowa is not. Sorry.
Next, realize that a Class III "license" does not apply to a person but to a weapon owned by a person. If the suppressor can be detached from the gun, then you are actually talking about two Class III weapons, a gun with a threaded barrrel to accept a silencer, and the actual silencer. So, you'll actually need two Class III "licenses." So, you'll be going through the process twice in parallel.
When you buy the weapon, weapons in this case, you will be disappointed because while you will fork over your money (about $1500 total in this case), the dealer will not hand you your new toys. Instead, the dealer will give you a pair of BATF Form 4 forms for each weapon. He will already have filled out his part on each. You fill out your part which is simple, name, address, etc. Where is asks for your reason for wanting the weapon, you write "collection;" they can't turn that one down. You'll need to get four passport photos taken of yourself. A pair costs about $10 so photos will cost you $20. Take your pictures and form 4s and appropriate ID to a local law enforcement agency that will do official fingerprints for you. Most police departments will do this, for a fee. Sherwood PD charges $20 per card to do this. You need two cards per weapon, so fingerprinting will cost you $80. Next, take this all to your county sheriff. The sheriff's office will have one or two people authorized to sign these. Call for an appointment ahead of time. Washington County Sheriff is fortunately very good about this. They will also afix the pictures using official glue a service for which they charge nothing. The sheriff's office is the only step of the process that doesn't cost anything.
Next, mail your four Form 4s, you with the four pictures attached all signed by the sheriff's authorized deputy, and your four fingerprint cards AND two postal money orders for $200 each to the BATF. It's best to go registered mail with delivery receipt.
Two money orders for $200 each? Yes. The federal tax on these types of Class III weapons is $200 each. Fortunately, it is a tax, so you can deduct it off your federal income tax if you itemize.
Somewhere between about three and six months later, you will receive your completed Form 4s by return mail (one for each weapon; the other is retained by the BATF). Notice the tax stamp applied to each one. Cool.
Get these photocopied twice each immediately and laminate one copy of each. Put the originals in a very safe place because you must have them to lawfully own the weapon. Put the photocopies with the weapons because you must have either the original or a good photocopy of it physically with you whenever you have the weapon on you.
Take the originals and one copy of each to your dealer. He will take one copy of each Form 4 and give you -- at last, six months and five hundered dollars later -- your toys! But wait, there's more... paperwork that is, receipts to be filled out and signed.
Congratulations! You are now a lawfull owner of a suppressed pistol. You must carry a copy of both Form 4s with you whenever you carry the weapon (and, in this case, if you carry the pistol without the suppressor, you still have to carry its Form 4 since the pistol, being fitted for a suppressor, is, itself, a class III weapon). If you take the weapon across state lines, you must notify the BATF. If you move, you must notify the BATF. If you move, you either have to move your Class III stuff yourself or ship in through a Class III licensed dealer. Selling the weapon must be done through a Class III dealer and the buyer will need to go through everything you did.
It's a big pain in the rear end.