Vaquero, Cograts to fatherhood! Your life will never be the same. As you're experiencing w/ home defense, you'll find yourself considering many things that previously gave you little thought. The most effective home defense gun is a shotgun. 12 gauge has been the traditional choice, but 20 is good as well. Choose whatever you and your family can best handle. And don't worry, it doesn't have to be a "tactical" shotgun. For many families, a youth model 20 is the best choice. You'll frequently see recs here for birdshot. Birdshot advocate have their reasons, but I agree w/ those who think who don't advocate. Birdshot at close range may cause a bad wound, but stopping power can be limited due to decreased penetration. Do your research and decide for yourself what you're most comfortable w/.

After shotguns, most folks would next turn to a handgun. I'd suggest a full size (e.g. NOT a compact or semi-compact) handgun in 9mm, 40 S&W, 357 Mag, 357 Sig or 45 ACP. All of these are similarly effective at stopping a fight, but I’d prob get a 9mm. Full size guns are generally easier to shoot for a number of reasons; you’re not looking for a concealed carry gun. Full size (not "airweight or lightweight") revolvers are fine, but they're not foolproof and have limited round capacity. Most folks would get a double stack magazine semi-auto (e.g a Model 17 Glock, S&W M&P, Springfield Armory XD/XDM and MANY other models). Of course, for someone willing to learn it's manual of arms, a reliable 1911 is always a good choice. There're lots of good self defense ammo available. One way to simplify the choice is to consider using whatever handgun ammo your local LEO's use. Put a premium on getting a 100% RELIABLE gun from a reputable gun maker, i.e. Ruger, S&W, Beretta, Sig, Springfield Armory. etc. This is NOT where you want to save money, especially for a handgun newbie.

Other options include carbine rifles, usually an AR-15 or a carbine chambered in a handgun round.

And yes, don't forego OTHER layers of home defense, including house dogs, security systems, security locks, etc.

Since you're not well versed in handguns, I'd consider getting some formal training, as well.

Carbines, shotguns and rifles will obviously require a larger case.

Since I'm also in the market for a small handgun case, I'l going to sit out now and observe that part of the discussion.