Make no mistake. I'm not saying that the Ithaca 37 was a bad shotgun. It wasn't. For many many years, the Ithaca 37 Deerslayer was absolutely the best slug gun you could buy. With a smooth bore and Foster Slugs, my brother use to get 2 and 3 nch groups at 100 yards, remarkable accuracy for its day.
But, the Ithaca 37 as a shotgun never enjoyed the reputation or following of the Winchester Model 12, or the later Remington 870 Wingmaster.
I have found that the Remington 870 Wingmaster, with its twin action bars, gives easy and positive extraction, and there is no binding or twisting since there is a steel bar on each side of the forearm. As for being smooth, after about 500 rounds, the Wingmaster is as smooth as glass.
Now, I'm talking about the Wingmaster version of the Remington 870s. NOT the plain 870s or the Sportsman 870s. Those actions are terrible.
If you want a relatively light, reliable, upland game shotgun, then I think the Ithaca will work fine for you.
Regards,
Mannyrock