You just rang my bell! I like those old guns, but I really can't say why. I have done a little bit of searching on the web and in books to get an outline of their history. I guess this is a good time to put what I have learned in writing, before I forget it all.
Beretta patented the design for their folding single-barrel shotgun in 1922, and it was available for purchase by 1925. It remained in production for almost 70 years, perhaps as late as 1992. It was not imported to the US all that time, though. It was very successful in Europe, and it has been estimated that Beretta sold aobut 500,000 of them. It was made in all gauges, 8, 10, 12, 16, 20, 28, 32, 36, .410, and 9mm rimfire. Most of them were very light, but it was also made in a heavier duck hunting configuration, and in trap-shooting models. Recievers were blued, nickel-plated, chrome-plated, case hardened, or gold-plated (on a deluxe engraved model). Most of the examples seen in the US had the opening lever in front of the trigger guard and the safety button in the front of the trigger guard, but some models had the release lever on the right side and some had a top tang safety.
From 1952 until some time in the late 1960's, Berettas were imported to the US by J. L. Galef & Sons, and during this time they were advertised as the Beretta Companion, although they were marked at the factory with the name of "Vittoria" (Italian name of the Roman goddess Victoria, goddess of victory, equivalent to the Greek Nike) along with an "engraving" of the goddess. The name "Companion" must have been copyrighted by Galef, not by Beretta, and when Beretta gave the importation rights to Garcia, Galef got M.A.V.I., another Italian manufacturer, to make a very similar gun and sold it as the Galef Companion. To this day, some people still think the Galef Companion was made by Beretta, but it was not.
Garcia, and later Beretta USA, sold variations of the gun as the FS-1, TR-1 Trap, TR-2 Trap, and Model 412. Importation to the US ended in or about 1988, but most of the guns seen in the US now date from the 1950's through early 70's.
In addition to the Galef Companion, there have been other copies or modified versions of the same basic design by other manufacturers. At least one of them was still available in Europe at least as late as 2006, and may still be available. The last manufacturer I am aware of who offered the same basic design was an Italian company called Effebi. The name Effebi is taken from the letters FEB, the initials of the company's founder - Dr. Franco E. Beretta. How's that for irony! The company was originally called by the founder's full name, but later changed to Effebi. My guess (but only a guess) is that Dr. Franco E. Beretta's distant cousins threatened to sue him for copyright infringement if he did not stop using the family name in connection with firearms.
These guns are very light and therefore have a tendency to kick. I have a 20 gauge that weighs less than 5 pounds and has a steel buttplate, and even with low-brass target ammo it will kick the livin' snot out of you if you are not carefull! Pressing it firmly against my shoulder helps, and I suppose a rubber slip-on recoil pad would help. I would not give one of these guns to a kid or a lady as their first gun unless I used extra-light ammo. I have found mine to be quite pleasant to shoot with Fiocchi Training loads (3/4 oz of shot at moderate velocity). You would be surprised how well that little gun and the Fiocchi Training shells will break sporting clay targets (but only one at a time, alas!)
Now, as to value: I bought my 20 gauge (blued receiver) via the internet for $110 plus shipping, and I think I got a good deal. A local gun shop had a 12 gauge with nickel or chrome receiver priced at $220, and it was sold, but might have been sold a little lower than the tag price. The Blue Book lists them at $80-175 depending on condition. They show up now and then on internet gun auction or brokerage sites at any price you can imagine, and some you can't, but the asking prices don't mean much because many of them fail to sell at all. I would estimate the market values to be $80-200, maybe as high as $250 depending on condition, receiver plating, and gauge. The most common gauges are 12, 20, and .410. I would pay the higher value for a nice 28 gauge - if you ever see one for sale, please let me know.