I'm late to this, but since you haven't mentioned already buying one, I'll throw in my opinio
Virtually any handheld shotgun is suitable for a 5'4'' woman, I've seen girls as young as 8 fire a 12 gauge. It's about form, not strength. as a 5'4'' adult woman anything you buy at the gun store you can handle.
I would look at a mossberg 590, with the 18.5 inch barrel and full under barrel tube mag, carrying 7 rounds. 12 gauge, I've seen people recommend that women get 20 gauge, and while 20 guage is just fine, I don't subscribe to the theory that women need less powerful guns because they're women, 12 gauge is fine, and more ammo is available.
for ammunition, 2 3/4inch shells, 00 Buck, they contain 9 pellets each roughly 1/3 of an inch in diameter.
however I have another recommendation, if you are willing to spend more money, like closer to a grand.
an AR-15 build rifle is a far superior home defense weapon to both a shotgun and a pistol, they are easier to shoot accurately, and can be equipped with rails to mount a flashlight. even better, the 5.56mm NATO cartridge is fired from the barrel at such a high velocity, and the bullet is so light, they will break on hitting most residential walls, reducing the risk of a stray round leaving your house and possibly injuring someone.
I found an ad for a New York SAFE Act compliant AR rifle, now to be NY compliant it has a fixed mag at ten rounds, and reloading quickly won't be an option, but at most you'll get seven rounds out of a shotgun, and NY limits pistol mags to 10 rounds as well, and with very minimal training you'll be much more likely to make those ten in your AR count and hit targets accurately. just submitted for consideration, hope this helps.
RUGER AR-556 5.56mm NEW YORK STATE SAFE ACT LEGAL AR-15 TYPE RIFLE - DD's Ranch
Also you mentioned concern about leaving loaded firearms, the standard for long guns is, you store with a loaded magazine and empty chamber. so my shotgun at my house has the tube full of shells, nothing chambered. if I need a round I need only pump it to be ready. and if you haven't already, set up an old cell phone on a charger, they can still call 911 and if the cell phone is always in the same place and you need to call for help, you'll always have it, like sometimes I forget and leave my phone in my car or a coat pocket or something, but my old flip phone is always on the wall next to my bed.