Back in 1969, fresh out of the Army I wanted to go deer hunting with my uncle. Now you need to know that growng up in our house the only gun I was ever exposed to was an old model 27 winchester SS .22. Dad didn't hunt as he only had one eye as the result of a childhood accident. He wanted to, but he also knew he couldn't see well. (side note...after 6 tries he got into the Army in '43 by memorizing the eye chart, lasted 27 days at ft. Dix)
Anyhow, after my military exposure to firearms, I was hooked and wanted to hunt some deer. NY state at the time only allowed shotguns in the southern portion of the state, so a shotgun was in order. I bought a brand new model 37 featherlight in 12 ga for the princely sum of $109.00, about two weeks wages. It took three years but I did score my first deer with that gun. Hunted with that gun for many years, until I moved to the north country, where rifles were the go to option. I've had 30-30's, (prefer Marlins), 308's, even an old Marlin 38.55 since but that 12 ga was the winner. Hold it tight and recoil wasn't too bad, and it was accurate out to about 75 yards with Brenneke's.
Alas the old Deerslayer is gone but was replaced by my uncles 1957 model 37 in 16 ga , which now resides with my oldest son in MD. Rather spend time with my handguns and old Savage 99's now.
Good luck with your 37, and show us some pics of the restore