Here comes the "this caliber is better than this caliber" arguments.
I've said it before, and I will say it again: the best caliber is the one you are most comfortable and confident in handling and are able to get accurate shots, as well as follow up shots with. If you don't know, then I suggest renting multiple handguns in a variety of calibers, and make your decision accordingly.
Shotgun is probably the best option but with kids at home I use my carry gun in a quick access safe. Btw it's a glock.26 9mm with Federal HTS 147gr HP.
Yes. If you don't believe a 9mm is enough cartridge, let me shoot you with one, and see if you think it'll do the job. A friend of mine in law enforcement once told me to put less consideration into the cartridge, and just find a gun I'm comfortable with and like shooting. Once I have that, then it's just a matter of practice practice practice.
Depending on your level of operational skill, such a large caliber may be unnecessary. There are highly trained operators here who have taken out entire brigades with wrist rockets and ball bearings. Govern yourself accordingly.
If you had to choose one and only one, make a trip to the range and rent both so you can see how they shoot. No caliber is worth anything if you cant hit what you shoot at. I personally sleep well knowing I have a 40, a 45, and a 380 loaded and ready to go, but I have shot all three and can hit with all three. Lots of debate about what the best close quarters weapon is, .45 versus shotgun, so pick your poision and get proficient with it. I drive my wife crazy because I also have the mossberg ready to go too. Shooting the 40 will have a little snap to it, more depending on what size of 40 you get, full size, compact or sub, but the 9 will feel the same way depending on the platform. I dont like subs in either category because because my hands are larger. So I prefer compact and full size. Good luck and let us know what you wind up with. Welcome to OSA.