$500 sounds about right, but it could be more or less depending on condition. The reblue and refinish is unfortunate, but not critical (unless you wanted to sell it exclusively as a collector, not a shooter). There's a mountain of 1897's out there and precious few of them could ever qualify as collectors - largely because of the sheer number of them still available. (16's are more rare, though.)
Don't expect that situation to change, either. This is one of John Browning's designs that are built to last.
By coincidence, my Dad left me an 1897 in 16 gauge, too. Mine was purchased new by my Grandfather and handed down from there. Value is something I've never considered before, as there's no way this gun will ever be sold - not now and not in a future generation, either.
Since you plan to shoot it, you should know that this gun was chambered in 2 9/16ths. Unless compromised by damage, the barrels are more than strong enough to handle the heaviest 2 3/4" loads for decades to come. But, using 2 3/4" shells will generate more felt recoil because the crimp is opening into the forcing cone and partially obstructing the shot exiting the shell.
If you care, you can get Gamebore shells in 2 1/2" from Kent Cartridge in Canada (contact "Fassteel" on this site). Besides being shorter, these are loaded for lower pressures, which also mitigates recoil. Used only for hunting, 1 or 2 flats of those should last the average hunter a long time.
If you get a chance, I'd love to see pictures of yours.