Welcome to The High Road, Joshua!
Sentimental value counts for a lot.
I don't know much, but if you're very new to shotguns, I can add that the
in the inscription means that it's built for the standard 12 ga shells that are two and three-quarters inches long, not the 12-ga Magnum loads that are three inches long (and which I prefer to leave to goose hunters).
You can do everything you'll want to do with 2 3/4" shells, I expect.
"Full" means that it has a "full choke." That's the constriction at the end of the barrel that affects the way the shot flies out of the muzzle. "Choke" can be none, or a little, or relatively a lot. The point of a full choke is to keep the shot in a tighter column -- the traditional definition of "full" suggests that the manufacturer intended that your gun put about 70 per cent of its pellets into a 30-inch circle on a target 40 yards away. Your mileage WILL vary on this, and the results will depend on how a particular load (
e.g., how much powder; how much and what size shot; even which company made the shells) behaves in your particular gun. Choke manufacture to produce particular patterns involves some science and a great deal of art -- or possibly witchcraft.
Oh: "Proof Tested" means that the manufacturer fires "Proof loads" -- shells with much more powder, causing much higher chamber pressure than normal -- through the barrel at the factory to be sure that the barrel won't burst or pieces fly off when the gun is fired with normal loads. The practice began long ago, before modern steels and manufacturing processes were available. Nothing wrong with proof testing even today. Don't try this at home, though.
Now you might have a gunsmith look it over to be sure that it's still safe to fire (probably will be; just a good practice to follow), and then go shoot it. I'll let my seniors here post our Shotguns Forum mantra.
Also, I don't know if you've been reading THR for a while or not; if you haven't, you might look at the "Patterning 101" sticky thread at the top of the Shotguns page, use the "search" function for others of Dave McCracken's excellent "101" threads and check the other Sticky for the old TFL threads, too. Be sure to come up for air once in a while -- there's a wealth of knowledge there, but one must eat and sleep.