OK, advice time, one by one-
The Winchester Model 1897 was designed in part because the receiver of the Model 1893 (the earlier version of the 97 design) proved not to be as strong as it needed to be to use the then-new smokeless powder that was coming into wide use. Only about 35,000 Model 93's were ever made, and there's a good chance its chamber is shorter than the now-standard 2 3/4".
The Model 93 needs special attention if you are to shoot it, it should be checked by a good gunsmith for mechanical condition and its chamber length determined accurately. If it is to be fired once cleared by the 'smith, it should be used only with shells of the proper length loaded with a powder appropriate to the design. It might be best to consider honored retirement for this one, rather than trying to make it a 'using' shotgun. There aren't a lot of 93s out there.
The Model 97 may also have a chamber shorter than 2 3/4", that will depend on when it was made (Model 97s were manufactured from 1897 until 1957 with nearly a million sold). This too should be determined by a good gunsmith, who should also evaluate its overall mechanical condition. There are a lot of Model 97s in use today in cowboy action shooting, but they are known to break parts and need a certain amount of nursemaiding under heavy use, even with the relative powderpuff loads often used in CAS. Talk it over with your gunsmith re. using this one, or retiring it too.
The Sears/Mossberg (the Mossberg 500 was introduced in 1961) should be no problem, so long as it is in good mechanical condition and used with shells of the proper length (the barrel should be marked in the area of the chamber as to the chamber size).
Make sure the bore is clear on any shotgun before embarking on a shooting session just on general principles, but especially one that's been in storage for a long time. Spare barrels for Mossberg 500s should fit it, if you want to add any extra barrels for different uses. See the list at
http://www.hoosiergunworks.com/catalog/cross_reference.html for one source to determine what compamy made various "hardware store" guns by model number.
Likewise the Remington- it should be fine for any 2 3/4" or 3" loads, except perhaps for steel shot. But make sure that the receiver is marked Magnum, the serial number ends in M and the barrel is marked for 2 3/4 or 3" shells. Were I you, I'd give Remington a call during business hours at 1-800-243-9700 to determine its date of manufacture (870s were first manufactured in 1950, Magnum 870s were introduced in 1955, well before steel shot was an issue, about ten million 870s have been sold so far) and ask if it's OK for steel shot, if you plan on waterfowling with it.
Older shotguns had fixed chokes, which are constrictions formed into the inside end of the barrel at the muzzle. Fixed chokes aren't visible usually, unless the barrel is really clean and you look down its length from the breech. As a rule, choke is intended to contain the spread of shot, but there are some negative or reverse chokes that are intended to spread it. Those are seldom seen, however.
Rifled barrels are for sabot slugs only as a rule. Smoothbore barrels can be used with shot or slugs, but rifled slugs are used in smoothbore barrels. Rifled slugs can be fired through full chokes but they usually work better in more open chokes (ImpCyl or maybe Mod). There are lots of extra barrels available for the Remington 870 too, be sure you get barrels with 3" chambers and with the same magazine cap detent in the barrel ring that Wingmasters use, if you go barrel shopping. The only 12 gauge barrel that won't fit is the one used on the 870 Special Field- the barrel ring on those is in a different place, because the SF had a shorter magazine tube.
That's a really nice collection of pumpguns you have there. The Model 93 might have some collector interest, I don't know much about collectible shotguns. No matter what anyone else thinks they are worth, I hope they are all priceless to you because they belonged to your grandfather.
That group of shotguns spans most of the era of American pump shotguns. The pump shotgun is a definitive American design, made to fit the needs of the working man with a limited budget. It's been adopted by armies and by law enforcement, but the overwhelming majority of pump shotguns see duty only in hunting blinds, the woods and fields, or on trap and skeet fields. And many a business or household in the USA is secured by a short barrelled pump shotgun as well.
I hope you enjoy them and care for them, and pass them along intact to the next generation in your family.
lpl