I currently own four 870's, three 12 gauges and one 20 ga. You really can't go wrong with them. I've killed a ton of turkeys and never had a problem with any of them. They're not too heavy or bulky to haul around through any terrain. If I were getting one today to cover your described range of uses, I'd pick the 870 Express Super Mag Turkey/Waterfowl model, #81125. It has a 26" barrel and comes with an extended turkey choke and waterfowl chokes. 26" is the most versatile barrel length you can get. It's not too long to be maneuverable for turkey hunts, but long enough for waterfowl, upland game, skeet etc. where you want more balance, you'd never get with a short-barreled turkey gun. If you ever want an extra barrel, Remingtons are easiest and least $ to find, even in the aftermarket. Same for choke tubes. I have 21", 26" and 28" as well as slug barrels for all my 12 gauges.
I've shot 3 1/2" 2 1/4 oz turkey loads. They produce recoil energy a few lbs. in excess of both the .458 Lott and .500 Nitro Express rifle recoils. I've never needed a 3 1/2" load to kill a turkey. I've killed most with 3" #5 lead, 2 oz. Federals and Winchesters. I also like #4's in these too. 3" Hevi 13's in #5's are devastating to turkeys out to 60 yds, and a lot of people like new Hevi-shot Magnum Blends 2 oz. for even better patterns at 1200 fps. I'll be trying some in a couple of weeks. The 3" turkey loads only kick a little more than a .416 Rigby., but I've never even noticed the recoil when I've shot a bird. LOL! .300 Win Mag has less than half the recoil energy of the 3" 12 gauge turkey load.
I've shot a lot of turkey guns and can't say I've ever tried one I like better than 870's. I'm not a big auto guy. I like the control of jam-free, lighter to carry, pumps.
Browning BPS's are heavier and pricier, but beautifully designed guns. If you've got the cash for it, go ahead and get the matte finished, dark satin checkered Walnut! (No reason to put synthetic camo on a work of art.) Novas and Super Novas would be high on my list, but their forearms can rattle a good bit, whenever the gun is moved to aim. I think they must have been designed by a waterfowl hunter, who wasn't thinking about bionic turkey ears. I like the 870's because the forearm is locked solidly, with no rattle, when the gun is cocked. Mossbergs rattle some too. I'd think there's nothing like having a gobbler slip in to 35 yards on a quiet spring morning, only to spook at the sound of a rattling forearm, as you carefully try to take aim.
That's my $.02.
Good luck.