I know that a Star gauge barrel is a fine barrel. Other than that, the fact that it's been sporterized detracts greatly from its numerical value. I've seen prices average from $500. to around $700. for them in that condition.
What you really have is a legacy from your Grandfather and a piece of family history. Value it and treat it well. In my humble opinion, don't refinish or alter it in any way. Clean it, lubricate it and by all means, shoot it.
“If ye love wealth better than liberty, the tranquility of servitude better than the animating contest of freedom, go home from us in peace. We ask not your counsels or arms. Crouch down and lick the hands which feed you. May your chains set lightly upon you, and may posterity forget that ye were our countrymen.” ― Samuel Adams