yep MO more than likely it is a 700 Rem and obviously the ol 06 is a warhorse and THE sentimental favorite big game caliber in this country. As for the condition, as long as it was put away clean, dry and the case was kept inside an air conditioned home that saw little variation in average temps and low humidity I doubt there will be any problems with the gun. For cleanliness and safety's sake (from the "keepin an heirloom in good condition" perspective) I would throughly clean the rifle inside and out, properly lube it (notice I said PROPERLY, not gobs of oil/solvent) and then take it too the range. I think you will find it ready for just about anything you want to do with a big game rifle and the fact that it was his will make it that much more special.
If only a box or two have been fired through it, the barrel is still basically "new" and should be treated as such, slow firing, don't overheat it and take your time while sighting in (words to live by for ALL guns really!) and you will have it when it's time to hand down too your son one day!
Good luck,
RA