If there's only one flight of stairs to the second floor both inside and outside, the logical thing IMHO is to prone out or otherwise take cover back from the top of the stairs, and wait for something to peek up over the top of the top step. Ideally there will be enough lights on downstairs, or good night lights, such that anyone ascending said stairs is backlit while you wait in the dark (remember the TF160/Nightstalkers motto?).
You can secure the entire family upstairs by covering the stairs themselves- make sure everyone else is assembled and on the floor behind cover too if possible, maybe the spouse can do that while on the phone to 911. If you have a natural choke point in your house, USE IT to your best advantage- no sense throwing it away by abandoning it to go prowling about the house if you really think someone's in there who shouldn't be. Actually you couldn't design a more easily defensible situation than to have all bedrooms on the upper floor with only one stairway for access. You'd want chain ladders installed under the windows in occupied bedrooms upstairs to allow for escape in the event of a fire, if that was how your house was built. As to other stuff...
My first vote is always in the "use enough dog" camp. Let the canine member of the family investigate strange noises, that's why you should have one- superior noses, superior ears... and teeth if necessary. My job in the event of alarums at home is to back up the dog (a 90-pound Brazilian mastiff) after she identifies the threat.
As to hardware, it makes relatively little difference which firearm you have IMHO. 'Use what you are best with' is what it all boils down to eventually. I prefer a 12 gauge pump shotgun (870s rule at Casa Lapin) with 00 in the magazine backed by slugs in the sidesaddle. An onboard white light is a help sometimes, but that doesn't mean you shouldn't have a separate handheld light also. It's bad manners to cover anything you just want to look at with your muzzle, after all. But it's good to know who you're about to drop the hammer on too. Shooting a family member by mistake is even worse manners. That's one of the other good things about having a dog in the house- they help with the IFF (identification friend or foe, aka target discrimination).
So what if the whoevers downstairs make off with your new teevee?
Well, so what? Secure your family upstairs, and secure YOURSELF up there too (aren't you more important to your family than a teevee?), behind whatever muzzle you choose to use. Let trouble come to you in a place of YOUR choosing- don't go looking for trouble where it can ambush YOU. Let the blue light cavalry worry about the downstairs. It might be a help to them if you affix a spare set of keys to a Cyalume lightstick and keep it available so someone can toss it down to them once the local LEOs show up (crack the lightstick before you throw it down so it illuminates)- that'll make it easier for them to get into the house without breaking anything.
Now think about this for a minute:
*A sure commo link upstairs- that is, a cell phone (landlines can be cut, or a thief downstairs can disable your upstairs extensions on the same line by taking the downstairs phone off the hook)- a working cell phone that can reach a tower, even one with no subscription, can still dial 911-
*Lights downstairs, dark upstairs (remote control lights, like the X-10 system, are nice, and so are 'power failure' lights in case the thieves pull your power too- but DOWNSTAIRS, not where you are)-
*All family members present, accounted for and secure behind good cover upstairs, with the 911 operator on the line, a good description of the house, the floor plan, and of the only armed family member's definite fixed location (can't very well give that if you are Ramboing around downstairs, right?) and reinforcements on the way-
*And you on point behind cover or at least concealment, at the natural choke point atop the stairs, with the firearm of your choice, a dedicated canine companion to nose out trouble- that pretty much IMHO adds up to a stacked deck in your favor.
Now tell me- would you want to give a crook an even break?
lpl/nc