The first thing to say is that if you chose to restore the sword it is very important that you get it done properly, it's a nice sword and it's coming on for four hundred years old so it deserves to be looked after. There are many people who say they can polish Japanese swords but everyone here will tell you tio avoid anyone who is not properly trained, we can recommend people for you if you go down this road.
The second point is that proper restoration will cost quite a bit, after the polish you will need shirasaya, a plain wooden sheath and hilt made to store and protect the blade. In financial terms this is not a sound investment but in terms of what the blade will become you might want to do it to preserve and enhance the family history. (I would want to just to see what is really in this sword.)
Have a look at this to see a sword in polish and shirasaya, please remember that this does not mean your sword is of the same value, this is just an example. https://www.aoijapan...amoto-kunishige
For the time being, and if you decide not to go ahead with restoration keeping the blade lightly oiled and covered, even if you wrap newspaper around the blade and tape it to make a temporary sheath, will keep it in good condition and prevent deterioration.
Hope some of this helps, let us know what you decide to do.
All the best