However, due to a recent increase in home invasions and robberies
I think an AR is about perfect for what you need. But I wouldn't trust a $550 AR for what you need. Once someone says "home defense", my requirements for reliability and quality go way up.
In that price range I'd say you're better off with a Glock or M&P, or a shotgun (and that's coming from a guy who hates shotguns for a use like this).
Whatever your choice, I'd definitely factor in the cost of a light and whatever it takes to mount a light into your cost.
