And here's another thing to consider. And don't take this the wrong way, because I don't live where you live, and I don't know the crime patterns where you live.
We don't get too many home invasion incidents around here. When we do, it's big news because it's unusual.
Here, the vast majority of home invasion incidents are dopers ripping off the other dopers, or they are somehow gang related.
The cops who respond to your incident may not be smart enough to figure out a legitimate case of citizen defending themselves because it doesn't happen that often in most jurisdictions.
So, be aware that they may have that perceptual bias. The experienced ones probably won't and the smart ones certainly won't, but you don't get to choose which cop(s) respond to or investigate your shooting incident . . .
I still think it's good to give a brief statement at the scene, if you have your wits about you, but then decline to talk until legal counsel is present.
I can't say this enough -- the more your actions conform to the way the police are trained to react when THEY are in a shooting, the better off you are.
You can only learn from experience if you pay attention!