I have some experience. I doubt your gun has crazy collector's value. The 12s are easy to come by and assuming it's a field model, not too rare. If it has a poly-choke there is no collector's value.
The 37 was, and is, a great gun. It's mechanics are different from the more modern BPS but that is the gun often compared to. Bottom eject, no gas or empties flying into your face or those of your hunting partners. Unfortunately, looks can be deceiving. Unlike the BPS it can be somewhat easy to jam and is very difficult to take apart. Forget a field repair of the action. Although I've never weighed one, they feel light and easy to carry when compared to other pumps.
If it has personal value to you, I'd shoot it, enjoy it, and save it for your kids or grandkids or nephew or whatever. Don't get scared off by it's "collector's value". I also wouldn't consider it a perfect go-to gun for whatever hunting situation may arise.