I vote 1100 over Saiga for hunting or trap and skeet, or one of the 3" capable autos. Sounds like you need two guns. 12 isn't too bad recoil in a gas gun. For women, I'd prefer a 20, they are reduced recoil because they are a 20, at least if they're fired in guns of equal weight. 20 gauge is more'n enough for home defense loaded with #3 buck 2 3/4" loads. It'll stop a man just as quick as a 12. Now, for hunting, I'd rather have the 12 tossing slugs. The 20 gauge slug is a little wimpy compared to the 12 on game. For all around versatility in the field, I'd rather have a 12. I own both, love my 20, but it ain't what I normally go for on waterfowl, especially geese, and it's not the hot set up for turkey if you turkey hunt. 12 can take anything a shotgun is normally used for and is available in goose loads that the 20 ain't. Lots of guys like 3 1/2" 12s on geese, but I just buy heavishot type loads in 3" and live happy when I goose hunt. They're more expensive, but I don't goose hunt that often now days. I don't know what the Saiga is chambered for, probably 2 3/4" only? That pretty much limits it for hunting, so going to a 20 gauge wouldn't be much more limitation IMHO. For all around hunting versatility, you need a 3" gun. I just picked up some new Winchester high speed 3" #3 magnum loads that should be MUCH better than the drylocks I've been using on ducks with my Mossberg. I'm looking forward to trying 'em out on the birds this season.
I'm addressing the hunting part of your requirements, though you list HD higher priority, because I feel any shotgun in any gauge, even .410, is good for HD and I'm not a trap and skeet shooter, just a hunter. My own HD gun is a 20" coach gun in 20 gauge and I'm plenty happy with it. I ain't Rambo, don't need a shot tossin' version of an M60. I hit what I aim at with a shotgun and an intruder is a heck of a lot bigger and much easier target than a dove on the wing at 30 yards. If I can't take out an intruder with my shotgun in one shot, I'm ready for retirement, hang up the shotguns. Just kinda how I feel about it. I'm good enough and practiced enough with a shotgun that a man ain't even a challenge. I ain't worried about firepower. I don't need no 20 round mag full of 12s.
If you ain't hit him in two shots, he's probably already stabbin' you to death anyway. And, coach guns don't jam. I do keep a Koplin butt carrier with five extra rounds on it, but I don't see ever needing 'em in the HD scenario. I ain't gonna go clearing the house with it anyway. It's a safe room gun, locked in my bedroom, blast him if he breaks down the door. He can have the danged TV if that's all he's after. I'm on the phone 911 behind the bed with the shotgun ready in case he's a real nut job. For me, that's how I see a shotgun. If I have to leave the room, it'll be with a snub revolver, easier to maneuver and harder to take away.