There are more important considerations than what gun or ammo. Really.
First, do all that is necessary to make your house less attractive to those who would intrude into it. That is largely the usual security and lighting any home security advisor would suggest.
Second, trim your list of friends who are sketchy, especially those who bring other unknown friends into your home without prior permission. That is the #1 way that a burglar or intruder discovers what is worth stealing - the homeowner allows them in and shows them what they want to come back for.
Therefore, keep the high dollar items out of public view, especially where they can be seen. Take a look yourself in your neighborhood, how many leave the garage door open and display their expensive tool chests and gun safes for all to see?
With all that done, then choose your favorite and most capable firearm. It needs to be short, easy to reload and fire. That means it should be a self loading action for single hand use.
Choose whatever caliber or cartridge you want, it won't make any difference. It will be too loud indoors, and it will penetrate the windows of the house across the street if it's inline with your front door if you are shooting back at intruders there with it open.
The two issues most ignore are noise and lanes of fire. Some suggest suppressors but for the working cost of acquisition, you could outfit your family with $150 Peltor Tactical Sport muffs and have not only the protection you need but also hear during gunfire. A typical suppressor for one gun is $200 + a trust + $500-700 on the low side of costs.
I've read snarky comments about "so you're going to put on a set of muffs when you hear breaking glass?" which isn't the norm. Most let the intruders in, or they are beating on the door. Do the other homework right on security and they can't break the glass even if they could get to it.
As for shooting lanes nobody maps out where they will likely be shooting and what will be behind them getting shot at by the bad guys. You DO have a responsibility to know where you shouldn't shoot, and lower penetration ammo is a nice thought. However the intruders dont' give a rip and will be blasting away with whatever they brought with them. Is your family going to be in a safe room that is actually safe, or are they just downrange of all the bullets flying thru the wall?
If you are chased into your safe room and they start shooting thru the door to disable the lock, will your cartridge be capable of returning effective fire?
What the cops use to reduce liability and prevent lethal injury to the potential detainee or innocent bystanders is not necessarily what a homeowner is restricted to using or even a good recommendation. This is the major fallacy of reduced penetration - it only means it affects you.
Food for thought, and a little practice walking thru your lanes of fire in the home will show what you can and can't do with the gun of choice and where you might need to make a different decision.