Get a 22 auto pistol, and a 38+P revolver.
A 22 auto pistol is a
required part of any gun collection. This is the gun that you will shoot the most, and probably also the one you'll be the most accurate with. If you introduce your wife to shooting with this gun, I KNOW she'll end up liking shooting. That's just how it works. If she's a total girly woman, she won't like shooting at all. If she's anything else, she'll probably like 22.
The recoil is gentle, and a basic target model is accurate and reliable.
A new 22 auto will run you around $300.
Then, get a 38 Special revolver rated for +P, or a smaller 357 Magnum revolver. A full size 357 Magnum, like a S&W 686 or Ruger GP-100 is probably going to be too big to be comfortable for your wife, unless she has big hands. After you get over your initial Magnumitis Thrill, you'll wind up shooting mostly 38 Special. 38 Special has more kick than 22, but not enough to be objectionable. It is the minimum revolver cartridge recommended for self defense, and has been in use since the 19th century. Cops used it from the early 20th century all the way up to the 1980s. A good +P hollowpoint is MORE than enough for a home invader. Models to look at are S&W Model 10 (basic 38+P, fixed sights, available used for $250) Model 15 (same as 10, but with adjustable sights; harder to find and more expensive) Ruger SP-101 w/3" barrel in 38+P or 357 Magnum (fixed sights, shorter 3" barrel will be harder to hit with at distances of greater than 10 yards) You can get a new one of these for around $500.
Don't get all excited before you go to the gun show. Sometimes, things cost more there than in a good local shop. Gun shows are mostly just good for used guns and gun accessories. Maybe reloaded ammo too. I've never seen a new gun at a gun show that I couldn't find for less by going to a proper store.
Maybe I'm getting ahead of myself. Do you even know the relative advantages and disadvantages of revolvers vs. autos? Autos have higher capacity, and faster, more accurate follow-up shots.
Revolvers are less likely to jam by the untrained. Just squeeze the trigger; it is pretty fool proof. No worries about certain types of ammo feeding reliably. No worries about a limp wrist causing jams. But reloads are slower and they take more practice to shoot accurately. They are also not as quick with follow up shots. But they can generally handle much higher power ammo, such as 357 Magnum and 44 Magnum.
Be sure to take ammo cost into consideration. A box of 357 Magnum near me costs about $26. A box of 38 Special costs $20. A Box of 45 ACP costs $20. A box of 9mm costs $14. A box of 44 Magnum, 44 Special, or 45 Colt costs $37. If you buy bulk online, you can generally shave a few dollars off those prices. But you begin to see why 9mm and 22LR are so popular.
Here's my Ruger SP-101, 357 Magnum, 3" barrel and a 7 yard group with the laser grip, fired single action:
The groups open up a little when fired fast double action, as one would when under attack. Still, it is good enough for self defense!
A 380 ACP, like this Bersa, is also a great choice. The guns cost around $300 new, and ammo is $20 a box, same as 38 Special. This gun is super accurate, light recoil, and has a very elegant shape, in my opinion. It has about the same power level as basic 38 Special, and is considered the minimum for self defense.
Size comparison with my SP-101, which is a compact revolver. I can just get my pinky on that stock grip; same with the Bersa 83:
Here's my S&W 625, in 45 ACP. It costs the same to feed as a 380 ACP or 38 Special, but has lots more power. Not enough to ever be painful though. If you're not going to carry the gun, this would make a perfect home defense and range gun for you, but will probably be too big for your wife: