Welcome to the forum, and congratulations on your sensible desire to purchase a Remington Model 11, a largely hand-fitted shotgun which would probably cost at least $2,500 per copy new today if it was still manufactured in the USA with the same materials, and to the same specs, and with the same hand-fitting that went into the guns that were made before 1948. Remington Model 11s can be purchased for incredibly low prices these days yet they are still rank among the finest and most reliable production shotguns ever made, and to this day they are still among the fastest-operating automatic shotguns. (Some mega-buck guns are faster, but those faster speeds are measured in terms of a few hundredths of seconds.) The steel parts hardly ever fail, and if they do, there are still a few places where you can buy parts so these guns should still be going strong when the plastic parts used in modern production guns have long since given up the ghost.
In my state I can use lead shot for everything but waterfowl. For waterfowl there are several options including tungsen.
One thing you should pay attention to is what length barrel you want and what kind of choke you want (unless you buy a gun that is already polychoked or put one on after you purchase.(Uggh! what an abomination to put on a classic old gun.) I have a 26" Improved Cylinder barrel and find it ok for most hunting, but I don't do a lot of goose or turkey hunting. If I did, I may have preferred a 28" or 30" full-choked barrel.