Great first post, and welcome to The Firing Line.
It is good to have people join up who are not afraid to do some research of their own from time to time.
I didn't read all the replies, just your posts, Jasper. Forgive me if I repeat something.
Remember that a 357 Magnum revolver can also shoot 38 Specials and a 44 Magnum revolver can also shoot 44 Specials.
You seem to be leaning toward a revolver, which is good. Less to go wrong, less to remember, and less upkeep.
Either one of these guns will be great for home defense duty. I'm with Bill, in that a modern 38 Special should be plenty. Modern ones can handle 38 Special +P ammo, which will be enough medicine, unless the intruder is armored. My feeling is that most of the time, the mere fact that you have a gun and a loud verbal announcment that you're about to use it will be enough to avoid having to use it. If I were a looter, I'd certainly look for an easier target rather than risk my life.
A revolver chambered in 44 Special would be a bit better because the bigger bullet is going to transfer more energy. But 44 Special ammo is expensive to practice with. Near me, it is $30 a box. 38 Special is about $16.
45 ACP is another good option. Maybe the best of the three I mentioned. Is has an even bigger bullet, but still does not kick too much. More energy than 44 Special. For home defense, you would keep full moon clips loaded for quick reloads. For range use, loading and unloading the moon clips would be a pain. Some folks just buy enough for all the ammo they're going to shoot, and load/unload them at home before and after. (45 ACP is a rimless cartridge, and as such, they need moon clips to make extraction quicker and easier in a revolver) 45 ACP ammo also costs less than 44 Special. It is about $20-25 a box near me.
To answer your question as to what you should do if your home is invaded while you're home, I'd grab the gun and a flashlight. The gun has more intimidation factor, so it is most likely to be effective without even having to use it. The flashlight will give you a tactical advantage; your attacker will be blinded. You've got dogs that will presumably wake you up in time to get your revolver & flashlight. That is what I worry the most about: not waking up in time to act. I'm a heavy sleeper. So's my dog, and I have no alarm system. On the plus side, I'm on the second floor of a condo, so most robbers would probably choose my downstairs neighbors instead of me.
Perhaps even more important is what happens with your guns when you are NOT at home. You mentioned that you have a safe. I recommend keeping them locked up when you're not at home. You'd hate to see your gun stolen when you're out, then used to kill someone in a later crime. Is your safe bolted down or heavy enough that it would not also be stolen?
What plans do you have for other family members with regards to the gun(s)?
Will the wife be trained? Are the kids responsible enough and/or old enough? Most of us here would recommend bringing the wife & kids with you to the range when they're old enough. I know CA has some pretty crippling gun laws, and I'm sure you've already looked into them.