With the exception of Thompson M1A1, all other weapons (and their ammo) can be bought. Here's what you can get in each type of shop.

[Basic Gun Shops:]
.38 Revolver
1911 Semi
Magnum
M1 Garand
Shotgun

[Giuseppe:]
Molotov
Magnum
1911 Special

[Harry:]
Thompson 1928
Grease Gun
MP40
Magnum
M1 Garand
K98 Rifle
Shotgun
.38 SMG
Grenade Mk.II
C96 Pistol


Here are all weapons listed in the (non-random) order they appear in your inventory. These names match the weapons in the video, and I included max ammo capacity as bonus info.

[Left:]
1. Fists
2. Grenade Mk.II (1/5)
3. Molotov (1/5)

[Up:]
1. Thompson M1A1 (30/90)
2. Thompson 1928 (50/150)
3. MP40 (32/96)
4. Grease Gun (30/90)
5. .38 SMG (30/90)

[Right:]
1. Magnum (6/36)
2. 1911 Special (23/69)
3. 1911 Semi (7/49)
4. C96 Pistol (10/50)
5. .38 Revolver (6/36)

[Down:]
1. Shotgun (8/48)
2. M1 Garand (8/32)
3. K98 Rifle (5/30)

Here's the easiest way to get a Thompson M1A1. Start the "Lost in Transit" mission in Oyster Bay (this makes a checkpoint and saves your location there). Reload checkpoint to exit the mission. Go to the nearby Clothing Store and make a mayhem until you get around 3 or 4 stars and a cop with an automatic weapon shows up (I think they're the ones that appear yellow on the minimap). That automatic is the weapon you want. Either before or after you pick up the weapon, hide in the clothing store closet until the alarm goes away, then steal a shirt to lose the wanted status, then run to "Lost in Transit" again to save the game, and thus save this weapon in your inventory.
This is the only weapon for which you can't buy ammo; you can only pick it up from NPCs who used the same weapon. So use your ammo wisely. Or at least get one kill with it.

TIP: Although the trophy description mentions "enemies", innocent civilians killed also count. The trophy popped for me when I headshotted a female pedestrian with a Thompson M1A1.