For starting your wife out in the shooting sports I'd recommend a .22lr. Find a used Ruger MkII or even a Ruger Single Shot if handguns are OK by her. Plan on spending a couple hundred bucks. Find a good NRA certified instructor, take a class with her, let the instructor do the work while you both listen and learn and have fun. Make it fun. Noise and recoil are low.
There are other .22's available to you but will cost more thus depleting your available funds (which is why my initial recommendations are what they are, cheap ammo costs = lots of practice rounds downrange).
Once she has developed a positive apptitude w/ a good beginning level firearm begin your quest for the next level.
HD? You've now got a .22 which is almost adequate to stop most thoughtful human beings who don't relish the thought of being shot, but we're talking predator control within your domicile here and that means someone who's obviously not in their right mind (to my way of thinking).
Handgun? Again, a lightly used .38/.357 revolver... probably a Ruger DA or maybe a S&W (they usually cost a little more).
Shotgun? You can have a lot of fun shooting clay pigeons besides depending on it for HD. I like 20 ga. but 12 ga. will let you buy light (reduced) loads (I haven't really looked for light loads in 20 ga.). New or used, it's hard to go wrong with a Mossberg 500 series, Remington 870 or Winchester 1300... tho for HD you probably want a shorter barrel in the 18" - 20" range.
So now you could own 2 or maybe 3 firearms depending on your shopping which would be fun to own and shoot and are dependable for HD and within your alloted budget. Well, maybe not at CA prices. I hear things seem to cost more over there for some strange (State gov't perhaps?) reason.
I too, wonder what the reasoning is behind your dislike for 9mm but that's really neither here nor there. I have several and find them fun to shoot and cheap to feed. To each his own. But do keep an open mind should your wife decide that a 9 is fine. Just feed it the hi-quality JHP ammo and remember placement, placement, placement, practice, practice, practice.
And welcome to THR. Please post more as your story unfolds. Have your wife visit Pax's website
http://www.corneredcat.com/ and read Pax's pearls of wisdom.