If you truly suspect someone's in your home, you should hole up, call the police and arm yourself, generally in that order as time allows.
The best defensive weapons in that situation are a rifle or shotgun, without question. AR-15 or 12-gauge shotgun---pump-actions will work but I prefer semi-autos and I'll explain why later---with buckshot is probably your best option.
If you insist on clearing your house yourself...Reconsider. The last thing you want to do is get blind-sided by someone. If you still insist...Well, it's your ***.
Some people still like rifles and shotguns for clearing rooms, and I agree...I'd suggest having your rifle or shotgun on a sling, for the simple reason that it's a lot harder to have your rifle or shotgun taken away from you and used on you when it's tied around you. You *can* use a pistol, obviously, but I'd try to avoid the "clearing rooms" plan of defense unless you've trained for it...In which case you'll also want to practice light-handling, use of cover, etc.
Other things to consider: guns are *loud as hell* indoors. We both have digital ear protection in the bedroom in case we end up holing up and arming ourselves while waiting for the police...During the following crap-storm that will happen, even after a *justified* shooting I'd rather not be recovering from hearing loss as well. Have a phone in your room as well, and one you can put on speaker is preferable.
It's a good idea to have a light on your firearm, and even more so if you insist on clearing rooms. A laser sight? Eh...One thing you have to worry about in a potential home-defense situation is shooting the wrong person, and it's easier to do with a laser cause you just see the dot...No real illumination of the rest of the target.
Finally, have a plan. Make sure everyone knows it. We have a few of them here, depending on who's home and such. Make sure everyone knows where the defensive firearms are. Make sure everyone knows where the defensive firearms they are most comfortable using are. Make sure everyone knows how to use them.
Make sure your hearing protection's batteries are good. Make sure your weapon lights work.
Pump-action shotguns: I have one for home defense, but I train with it. Until and unless it's muscle memory for you to cycle the action and fire, a semi-auto shotgun is a better option, IMHO. Yes, they're more finicky on ammo, but if you pick a semi-auto shotgun and run the same defensive ammo through it, set it up for that ammo and don't mess with it.
If you go with a pistol, don't buy in to the caliber myths. 9mm, .40S&W, .45ACP...Any of the common center-fire pistol rounds will be effective if you hit someone in the right place with them. My Glocks are chambered in .40S&W, mostly cause I got good deals on the pistols...If I had it to do over, they'd probably be in 9mm. The extra mag capacity of 9mm is, IMHO, a bigger asset in defensive shooting than the heavier weight of a .45ACP.
Practice, practice, practice. Running a few boxes of ammo a year through your defensive guns at fixed targets from a fixed position in a well-lit shooting range will get you started, but you'll be inadequately prepared at best. Take a defensive shooting class or three from reputable instructors. Consider doing some practical shooting competition to see how the stress---of even just a "game"---affects you.
