I'd go one of three ways w/ order in *my* personal preference:
Pump shotgun, not as maneuverable as a handgun but plenty accurate, esp for the application. Can use several "less than lethal" rounds such as bean bags or rubber pellets, so your fiance's mind may be eased a little. NO intruder wants to hear the sound of that forend chambering a round. I load the first 2 rounds with bean bags, alternating 00 buck & slugs after that for my home shotgun. Prefer Remmington 870 or Mossberg. New $200-300, used ~$200 or so
Revolver, mine is S&W in .357 w/ 4" barrel but see what fits you and yours best, plenty of stopping power, you can practice using .38s making it cheaper to practice with. Yeah, it doesn't hold 17 rounds, so what. If you don't hit or scare an intruder off with 5-6 rounds, what makes you thing the next 10 will do any better. They are ultra-reliable, will not jam, if you had a bad round - pull the trigger again. New $400-600, used ~$300-400
Semi-auto, probably Glock or Springfield XD for the lower price ranges and still a good pistol. 9mm will be just fine as would .45. I too have a 10mm as noted above but rounds are expensive so practicing gets expensive. These weapons usually hold 10-19 rounds, good & solid weapons, relatively cheap to practice with. Jams are a possibility but a remote one, bad rounds must be cleared which would be horrid in a life n death situation, although this is indeed quite rare with good ammo. New $500-600, used $350-450
For any handgun round, use the safety slugs (as noted above) or frangible bullets so they don't go through walls and into your neighbor's house.
Take training classes or join a gun club at a local range if available, local gun clubs usually offer several courses of training from simply familiarity to home defence to tactical courses. Practice practice practice, this is also where the local range comes in handy.
Ask your local PD for advice as well, they see this kinda stuff far more than most and will usually have good advice.
While I like shooting, one is *usually* as well served by making a ton of noise if they hear an intruder in the house. A whistle or clanging of anything will let the intruder know someone is awake, this itself would drive off most. For the rest of 'em, let 'em know you're armed by racking the forend, slide, or cocking the hammer. A firearm can often be used as deterrent as much as a weapon.