I would suggest ordering a " Range Rod ", which is a one piece, or solid, metal rod, and a 12 gauge jag, plst the patch pulling jag, and the ball pulling jag for it. Once you have the patch jag in hand, use a micrometer to measure its diameter. When the gun arrives, use a micrometer and old fashioned calipers, or a dial caliper to actually measure the inside dimensions of the barrels. That will tell you how thick the cleaning patches should be, and give you an idea how thick a working patch you can use with a RB load.
Then you can order the proper wads, and patches. I use 3 inch diamter round, or 4 inch square cleaning patches in my 12 ga. I also have a cottom swab fitting for my range rod, and I use it with the cleaning patches, rather than with a jag, unless I think I need to clean out plastic or lead. I also recomment you buy a 12 gauge bore brush to fit the rod. Next to the swab, I find the brush is the must used fitting I have for the rod.
If you go back through the Smoothbore section, or do a search about shotgun loads, you will find recommendations from Iron Jim Rackham, To use only Overshot( OS) wads to load the gun. He recommends using a puch or awl to put small holes in the outer edges of the wads, sot hat they allow air to escape as you are driving them down the barrel. He uses 4 OS cards on top of the powder, aligningthe holes in each card at 12, 3, 6, and 9 o'clock so that together they provide a good gas seal. then he puts in his shot load, and then two OS cards on top. For hunting, you take so few shots, there is really no need to lube the barrel or wads. For target shooting, where you do need to keep the fouling soft, some shooters use a dolop of grease on the bottom side of a 5th OS card which does down on top of the first 4. Others simply run a lubed patch down the barrel after the final OS cards are run down on top of the shot, to lube the barrel. Either way, the experience of Mr. Rackham, and others here is that they get much rounder, and fuller patters from the open cylinder shotguns.