Half Sigma recommends the Remington 750.
It looks like a friendly hunting rifle with the wood finish, so it won't make juries think that you're some kind of vigilante military nut. But it's good for 5 shots, so in case you miss once, or there is more than one criminal invading your home, you have 4 more shots.
But remember: it's better to just let the criminals just take some stuff rather than shoot them (the cost of hiring a criminal defense attorney is a lot higher than the cost of replacing whatever they are going to steal from you), and never shoot anyone in the back because that doesn't look like self defense.
* * *
Peter provided a link to this article that supports my choice of a semi-automatic rifle for home defense.
IS .223 BETTER?
Some commenters have convinced me that the .243 rifle might be too powerful and you might be better off with a .223 semi-automatic rifle like the Ruger Mini 14 Ranch Rifle. The version with the wooden handle has a very traditional non-military look to it, good for creating the impression that you're not some gun-nut-militia-survivalist-vigilante type.
There's a version with a 20-bullet magazine, ideal for taking down a small gang, but that may create the wrong impression. "Who would need a 20-bullet magazine to go hunting? He must have been planning a massacre."
Less expensive and less powerful is the Ruger 10/22 series of rifles.
Some say that .22LR isn't powerful enough to stop a bad guy with a single bullet. On the other hand, it's least likely to cause permanent hearing loss if used indoors without ear protection.