For home defense, I would strongly suggest a handgun. Something on the order of a medium frame revolver with a 4" barrel. S&W, Taurus, Rossi, Ruger are all good quality. Rossi and Taurus are at the lower end of the price range. Shotguns are impressive looking but not so good for home defense. Try this, take a broom, hold it to your shoulder and move through your house pointing it at every door, window and down each hallway. In most houses, this will be quite cumbersome and leave you in an exposed position.
Also, the "Aim in the general direction and a shotgun will hit the target." is wrong. At 25 feet, the pattern on most shotguns is just 3 to 6 inches in diameter. I know as I have fired test patterns on many shotguns with various amounts of choke and various loads.
The noise and muzzle from a .357 indoors in the dark is blinding and incredibly loud. A .38 special loaded with +P ammunition is noticibly better, but still loud and bright.
Glaser and Cor Bon both make handgun loads designed to prevent over penetration.
http://www.dakotaammo.net/products/glaser/glaser.htm
Also, for several years it was popular for some in the media and Brady types to bring up a "statistic" that people with a gun in the home were 43 times more likely to be shot than someone without a gun in the home. That "study" was done by a Dr. Kellerman at Emery University and was shown to be wrong as Kellerman was data mining.
A big dog is fine unless the intruder isn't afraid of dogs and/or has a gun. If Mr. badguy shoots your dog, what do you do next?
A trigger lock is really not necessary. If you want to make your gun inoperable, just take it apart. If it is a revolver, put a pad lock through the top strap. There was a gun lock that worked similiar to a thick rubber band that could be removed by an adult in a second or two. If those are still available, they might be worth a look. My wife and I have each used a handgun for self defense, one incident each. I would not have had time to remove one of those key ooperated trigger locks before the bad guy could have done his harm. My wife might have had time, assuming the key was right there by the handgun when she needed it.
If you do get a gun, practice, practice and practice. Practice in good light, bad light, with either hand, sitting, standing, kneeling. Run a 50 yard sprint or do 20 jumping jacks then shoot. The sprint gets your heart racing and simulates the adrenaline rush you have to deal with when using a gun for protection.
Best wishes.
JA