You can't go wrong with either a pistol or shotgun as a first/home defense gun. I would personally buy the shotgun first, and as far as your wife shooting it, if she has to use this gun while your gone the adreniline running through her will be more than enough to fire a 12 gauge. Either the mossberg or the remington are good first choices, both offer great reliability and reasonable price. My personal choice is the remmington, more aftermarket part options.
As far as a handgun you need to go to the range with friends or a shop that rents handguns and see what you and your wife actually like to shoot, stick with a reliable brand. My personal choice is H&K because I like the feel of the gun in my hand. I would stay away from anything smaller than 9mm, my personal favorites are 40s&w and 45acp. Welcome to the world of shooting!