I too have a JC Higgins Model 31 I got new as a kid in about 1958 or 1959. I also picked up both period correct scopes for it later, the J.C. Higgins Rifleman and Rifleman Jr. While they are a very fine rifle in their own right, they have not drawn much collector interest or value, so getting the right information on them is a huge undertaking. I took it on some time back... and only accepted what I found reference to in at least 2-3 places.
These rifles were made by High Standard for Sears from 1953 to 1962, and supposedly in 4 versions (583.70, 583.71, 583.72, 583.74) that included up to engraved models. But even that is not totally correct, because my rifle is a 583.75 (does have the sling, maybe better wood, fit and finish, but not engraved). As far as I have ever been able to confirm, they are not a model that High Standard ever listed in their lineup for sale under the "High Standard" name, but rather a contract gun made exclusively for Sears under the J.C. Higgins moniker despite some references to the HS mod 31. IE, the JC Higgins moniker was generally used for contract guns made for Sears from 1946-1962 by Browning, High Standard, Marlin, Mossberg, Savage, Stevens, Winchester, etc. Some were standard models already offered by those companies, but with less frills so they could be sold cheaper by Sears to be more competitive (lower quality wood, finish, features, etc). But not all of them... some were models made just for Sears.
Value is a product of supply and demand, but even that is speculative as there is not much interest in these by collectors. Too bad as it is a very finely made rifle with huge ammo capacity, is very reliable and way accurate enough for serious hunting and not just plinking. Mine is as clean as it was the day it was bought and still functions flawlessly. I never did get around to mounting the scopes on it though - not sure what is the correct period mounts.
None of this is etched in stone folks, just what a ton of research turned up abbreviated in a nutshell. Regardless, a fine rifle well worth what ever you have to pay for one if you want to shoot an old school semi auto that was probably mostly hand made and so will probably last several lifetimes.
Larry