I agree with jakemccoy. I would honestly discuss this with our wife, slow things down and save up $750 or so to pay for the gun, ammo, cleaning supplies, small safe (like a Gunvault) etc.
On a tight budget, a revolver has some big price advantages over autos when you consider the number of test rounds you need to fire with your chosen defensive ammo is MUCH less with a revolver. Good hollowpoint ammo gets pricey (an average of $1 per round), and firing 100 to 200 rounds of it in an auto to verify feed/extraction reliability obviously gets expensive. That's assuming you can find that much hollowpoint ammo in a single brand to test these days. OTH, with a revolver you can get by with only a cylinder or two full just to make sure the cases don't stick in the cylinder.
As for makes/models, I picked up this 4" .357 Magnum Ruger Police Service Six for $275 a few months ago. I recently saw a TON at a gunshow selling for $280-300. These come from LE agencies in Canada, as I think they just did a big trade in. I love mine, and wouldn't hesitate to buy another to pass down to my son when he turns 21. This is a very versatile gun, as it can shoot everything from 200 grain hardcast .357 Magnum loads for hunting big scary animals all the way down to 38 Special wax bullets for cheap (if messy) practice (a primed case with no powder punched into a bar of parifin wax). I'm about your size (6'7" and 210 lbs), and find the gun remarkably easy to conceal carry with a good belt and holster, should you decide to go that route one day.
Other options include used S&W Model 10s and 64s (fixed sight .38 Specials, blued or stainless respectively) which can be found for low $200s if you are very patient. Either makes an excellent, reliable home defense gun for beginners and pros alike.
But for home protection, it's tough to beat a good pump shotgun. I know you said you live in an apartment, but then again something like #4 buckshot from a 12 or 20 gauge actually penetrates fewer walls (typically) than many medium and big bore handgun rounds. The only big drawback is the need for a bigger, pricier gunsafe, being that you have very young kids around that don't understand concequences yet.
In the end I have both options. I most certainly prefer a shotgun though, a 12 gauge Mossberg 590 pump loaded with 00 buck. There is just something extra comforting, knowing you can hurtle 9 .33 caliber lead balls at a badguy threating your life and the lives of your loved ones with the single pull of a trigger. God forbid it ever comes to that.
