In general, the safest thing you can do with having kids and guns in the house is to teach the kids (when ready) everything about gun safety. Teach them how dangerous they can be, the 4 rules posted above, etc. People that are afraid of guns don’t teach their kids anything about gun safety, and their kids have no idea how to handle a gun properly as a result.
As a carrying concealed weapon permit holder, I was taught at a young age how to handle guns, went through a training class with my dad, and we regularly went shooting out in the wilderness or at a range with handguns, rifles, and shotguns. Because of this, I am (and have always been) extremely safe with guns. I have been shooting with friends who were not brought up this way and they are a danger because they don’t posess the knowledge it takes to responsibly handle a gun. So basically, the best tool is fighting ignorance and teaching safety.
All this being said, in the OP’s case, I would buy a secure case that can be unlocked very quickly. But more importantly, it doesn’t matter much what handgun you buy - buy one you are comfortable with and PRACTICE. A well placed shot from a .22 caliber is much more effective that a wild stray shot from a .50 caliber desert eagle. So the best thing you cna do is shoot your gun regularly and often, so you know it very well. So well, you can confindently handle it in the dark by feel when being terrorized and frightened by a vandal. it must become second nature. That’s the key to whatever weapon you choose - don’t just use it when you have to, KNOW HOW to use it when (if) you have to.
Also, don’t be immediatly turned off by larger calibers and thinking they are “too big”. I have seen many women on the range firing .45 colt 1911’s with no problem (thats my handgun of choice). No matter how small you are, if you practive proper form, you can handle nearly any gun you want. But above all, just feel very comfortable with the gun you choose and practice, practice, practice.