Short answer: I own other shotguns, but I USE Benelli Supernovas. I have two set up for calling, same exact set up, except one has a 28" standard barrel, the other has an 18 1/2" aftermarket barrel. Both have +2 mag extensions, standard stocks with an elevated cheek-piece, B-Square Saddle Mount optic rails, bipods (and adapters), and tru-glo open red-dot sight. Both shoot 00buck out of light modified chokes.
Long answer for new guys that describes how I got there:
The ideal shotgun will vary from shooter to shooter, but here's how it cuts out for me.
GAUGE: 12ga only for me, usually in 3 1/2", but often in 3". I shot 2 3/4" for many years as that was all I had, but now, I'm using as much as I can. I own a 20ga to let other guys/girls borrow it, as well as a pair of 16's, but I'm a 12ga shooter.
LOAD/CHOKE: My standby has been Winchester Super-X 00buck through a light modified or improved choke for as long as I've been hunting. When I started, I picked it because that's what dad and grandpa gave me, fast forward to today and it still works, so I still use it. I really like/liked the Hevi-Shot Dead Coyote load out of a Carlson's Dead Coyote choke, but at $4 a shot, no thanks. Any buckshot, 4 on up to 000 (I guess BB and T can play too) will work. Depending on your shot size, you're talking about energy somewhere between a .22lr to a .22WMR on EVERY PELLET, and there's between 8 to ~60-70 pellets flying at once, no wonder shotty's are so devastating.
SIGHTS/OPTICS: I like open sights (tru-glo clamp on's work better than you'd expect) or open red-dot sights for a predator shotgun. When a dog backdoors you and you need to wheel around and deliver a shot on a runner, I want something fast handling with a continuous field of view. Fiber optic sights and red-dots are very functional at night as well. I use Tru-glo open red/green dot sites, they're cheap, and work very well.
OPTICS MOUNT: I use B-Square mounts because I could find one on a shelf (and it doesn't require me to D&T my receiver). At the time I wanted a bolt on rail (like the turkey versions come from factory), but in hind-sight, I'm glad I have B-Squares because I can pull them off and go wing shoot for fun, then strap it back on and go call that evening, all it takes is removing/replacing the two action screws. I bedded mine with automotive epoxy so it goes back on the same every time, just to make me feel a little better about it.
BARREL LENGTH: Depends on the purpose. In a primary calling weapon (i.e. rifle is at home), I want a long barrel for max range. In a backdoor gun (i.e. I'm sitting over the rifle, but need a sweeper if one comes in behind), I want a short barrel for maximum portability and easy handling. I have a standard 28" on one Supernova and a Carlsons 18 1/2" on another, to suit both applications (used to just swap barrels, then I bought a used Benelli action).
BIPOD: I run bipods on mine. Benelli Supernovas have sling studs on the bottom, instead of the end of the mag cap I make leather, epoxy, or nylon adapters to fit harris standard bipods on
CAPACITY: I like having as much capacity as I can. Whether it's a matter of not needing to reload between sets, or having as many shots as I can get, I like capacity. With a +2 extension, the extension is about even with the end of my 18.5" barrel, and I can run 5+1 3.5" (or 9+1 2.75"). I've ran 6 shots of 3.5" on a triple before, so I was glad to have it.
TRIGGER: Probably overlooked by 90% of guys. Just like a rifle, I like to have a good trigger. I don't want anything super-light, but if I need to hold steady on a 70yrd shot, I want to know my trigger control isn't an issue.