Sammio,
Sorry I forgot to welcome you to THR earlier- glad to have you aboard.
It's always hard to get a gun by inheiriting it from someone you loved, but it can be a good way to remember someone. I have my grandfather's vintage 1929 Winchester Model 94, and I treasure it immensely. I have no children of my own to pass it on to but it will go to one of my cousin's children who will treasure it also. I haven't shot it in decades but I recently inspected it to make sure it was in good shape- and it was fine.
It doesn't hurt for a gun to sit unused as long as it is properly stored, it won't ruin or go bad as long as it is taken care of. It is best not to store a gun in a case, as that can hold condensation against it and make it rust. It should be stored in an area where the climate is controlled, outbuildings, basements and attics are not necessarily good places. A closet can work well.
There are various approaches to storing guns which will not be used for a time. I like to do it this way- First be sure to write down the make, model and serial number on a card or paper. I field strip the gun to be stored and give it a good cleaning, coat inside metal surfaces with plain petroleum jelly, reassemble and release all possible springs (in this case, make double sure the chamber/magazine is empty, push off the safety and pull the trigger so the hammer is at rest). Then lightly but thoroughly coat the wood surfaces with Johnson's paste floor wax- if you get it on the metal it will not hurt and can actually help. I also coat exterior metal surfaces with a light application of plain petroleum jelly. Then I wrap the gun completely in waxed paper, wrapping it in form-fitting fashion. It is good to pad sharp edges (muzzle, sights, bolt handle) with swatches of wax paper as you wrap to keep the wraps from tearing as easily. I use masking tape to secure the wrapping.
I then add a wrap of butcher paper, or plastic lined freezer paper, with the plastic side inside, also secured and completely sealed with masking tape. I write on the outside of the butcher paper the make, model, serial number and origin plus any other information I have about the gun with a permanent marker. This will allow you to store the gun without attention for years. It had been about ten years since I last put my grandfather's gun in the back of the safe wrapped in this way, and it has not deteriorated at all.
If you want to display it instead, there are numerous ways to do that. But security becomes an issue for guns on display, they are a favorite target of thieves. It is difficult to display a gun so that it is secure from theft. We keep no firearms at all visible at home, though we would like to be able to do so here (the air rifle over the back door doesn't count).
I hope you can find a way to keep your dad's shotgun as an heirloom and enjoy having it. It is an unusual gun and marks a step in the development of Remington's semiautomatic shotguns, from the Model 11 (recoil operated, the Browning design) to the Model 11-48 (also recoil operated but streamlined) to the Model 58 (Remington's first gas operated semiauto) to the Model 878 (also gas operated) and culminating in the introduction of the Model 1100 in 1963 and its evolution into the Model 11-87 25 years later.
Regards,
lpl/nc