Typically, the only kind of refurbishing of a vintage or classic gun that should be undertaken is a proper restoration. Any refinishing or "improvement" that isn't true to factory original may serve to increase the value of the piece, but isn't likely to increase the value beyond what was paid for the work (if even that much).
I wouldn't expect to recover my costs from a professional restoration, either. Although, if a "best" gun can be purchased cheaply enough and doesn't suffer from serious mechanical issues, it's certainly possible to make a tidy profit if all the stars align perfectly. I would consider such opportunities to be somewhat rare.
While I personally love Winchester 1897's to death (I own several), I would not consider this model to be a candidate for profitable restoration, regardless of the condition of the prospect gun. Even in immaculate condition, they simply aren't worth enough to cover the cost of the work. Add to that the fact that most collectors of this model want the gun to be in original factory condition, not refinished in any way.
CAS shooters make up a substantial market for the 1897, too. But, they're more concerned with price and shootable condition than they are about metal and wood finishes. Their price sensitivity means that they don't constitute a viable market for restored 1897's, either.
Unless you want to refinish the gun for your own aesthetic enjoyment, I can conclude with full confidence that refinishing and/or restoration is not a profitable proposition with this gun.
By all means, be sure that the butt stock is in satisfactory condition before using the gun in competition or for hunting. If that requires a new stock, aftermarket duplicates are easily available. They'll make the gun safer and perhaps more reliable, but they won't do much to improve the value.
FYI, most of the early production of 1897's (up to about 1920ish) were chambered in 2 9/16ths. No problem with nitro (smokeless) shells in these guns, but you'll get less recoil and better shot patterns if you use 2 1/2 " shells. Using the correct length of shells will generate lower pressures because the crimp won't obstruct the forcing cone. This will reduce the stresses on the gun, which is important for longevity.
As you probably know, the takedown versions of the 1897 are blessed with a clever John Browning adjustment feature. What many people don't know is that there are 6 progressively more offset replacement sleeves available.
One of my 1897's has been in my family for 3 generations. It took 80 years for that gun to loosen to the point where adjustment sleeve #2 had to be installed. At that rate, the gun could last up to 400 more years, even with regular use (using subsequent sleeves). AFAIK, my dad didn't know not to use 2 3/4" shells in the gun. Had 2 3/4" shells never been used during the first 80 years, the gun may well have gone 120 years before the second sleeve was needed.
These sleeves are, of course, simply user-installable maintenance. Just like all other gun designs, "repairs" are also an option after further adjustment is no longer practical. Clearly this incredible John Browning design will be around for people to enjoy centuries after we're long gone.
