I LOVE Model 37s. I learned to shoot shotgun on my Dad's 1950s 12 gauge 37. Now that he's gone, I've got it.
The only problem with the Model 37 is its light weight, which means you need to invest in recoil reduction devices if you're going to be shooting it a lot.
The absolute WORST recoil experience I ever had (and I've shot some truly monumental thumpers, aka British big game cartridges) was with Dad's 37.
Friends and I were doing some informal trap shooting, and somehow I had managed to mix a 1 1/4 ounce slug in with my light trap loads.
I dropped it in the gun, pulled up, and let fly. It was a hot day, so I was only wearing a thin shirt, the 37 only had the plastic butt plate on it, and worst of all, I didn't get the gun seated into my shoulder.
It hit me so hard I greyed out a bit from the pain. I later developed a bruise that went down my chest and down my arm almost to my elbow.
I ran the trap that day because I couldn't shoulder or shoot anymore after that.