Would a pistol or rifle be better for home self-defense?

Some really great advice here.
I worked as a retail salesman in gun stores and finally got my FFL and opened my own shop. Whenever a customer asked your question, the very first question I asked was "Are you prepared to take a life?" Many answered no, they only wanted to intimidate. I then suggested Mace or pepper spray. Lost some sales that way, but I have to sleep at night.
If the customer was convinced a gun was necessary, I then suggested a firing range that rented firearms. Go and find out what you and you wife are comfortable with. Lost more sales.
Finally, with a customer that still wanted to purchase a weapon, I pointed that my weapon of choice in my house was a Winchester Defender 12Ga loaded with 6 rounds of double-ought buckshot. That will take down any man alive (also big bears). If your wife is not comfortable with that, get a 20Ga or even a .410.
Good luck and I believe you are showing some good common sense.

Remember one very important thing you better be sure you are ready to kill, if you hesitate you die.

I Will Give You My Two Cents About Defending Your Home.
I Have Defended My Home Against Two Legged And Four Legged Animals Since I Live In A Rural Area Now , But I Have Also Lived In Cities.
Any Encounters You May Have Will Be At A Distance Of 8-15 Feet And If You Are Inside Your Home Over Penetration Is An Issue, So Any Rifle Should Be Out Of The Question, Most Handguns Should Also Be Ruled Out Except A Revolver That Shots .410 Shot shells And Put A Laser On It, If You Put A Red Or Green Dot On Someone’s Chest That Can Be Very Intimidating And Should Scare Most Dirtbags !
My Choice Is A 12 Gauge Pump Shotgun Loaded With Triple Ought Buck Shot And Since Most Modern Shotguns Have Pic Rails You Can Also Put A Laser On Them, If You Think Your Wife Can’t Handle A 12 Gauge Get A 20 Gauge Or A.410 Pump Action.

Whatever you're confortable with, and operate proficiently.
Nothing to updated, an old shotgun that doesn't cost to much, or even a 22lr rifle, better then nothing.
Many will say a 22lr isn't good enough for home defence, but I learned, Round Placement is "KING".
As a police officer for 21 years, I had a case when someone shot another, that entered his home at night. He shot the guy in the knee, and it stoped the individual, untill the police came. I had two other incidences when they were shot with a 22lr rifle, and both died.

If you don't feel good at shooting someone, then a firearm might not be a good choice for you, try other means without a firearm, like a sign that reads, "Shotgun Lives Here".

Deterence is the better choice, prevention is key, better then ATF (After The Fact).

Do I have firearms at home, YES.
Do I have a shotgun and 22 rifle, YES.
Do I have a outside sign, YES (You Are a Target).
Do I have a deterent, YES. (6 seccurity cameras) and a Dog, YES, barks at anyone that comes to the house.
Did I ever have to shoot someone at my house, NO, but a few time they saw me with a firearm, and that's all that was needed.

It's your life, "Take Care of It"

Ultimately you go with where your skillset is and what you are comfortable with. If you have little to no experience I would start with a rifle or shotgun. Easy to control and easier to aim. Yes, a pistol is better in close spaces but with your limited skillset you aren't room clearing at this point. You just want something you can use accurately and safely without hurting yourself or your family. A simple 9mm pistol is a good start as well. You already know the basics. They don't really change. I would start with a long good and add a pistol after that. Get some range time and learn how to do maintenance on them.

Personally, shotgun all the way, very little issues with over penetration (unless you are running slugs), pellet spread will cause wounds. Hope to God that you will not have to use it but just to have it is a sense of security.

So far the recommendations are 100% in favor of a shotgun -- I'm not going to disagree with choosing a shotgun but I will quibble with a few points.

While a rifle and pistol each require more training than a shotgun, using a shotgun effectively still requires both training and practice. Do not fall for the idea that a shotgun doesn't require aiming -- at home defense distances the entire spread of a 12 gauge shotgun load will still be less than 12" and you want that 12" spread to be entirely (or at least mostly) on the intruder's chest.

Regardless of the weapon you choose, tactics are much more important that the weapon. The first step in home defense is HAVE A PLAN. I'm sure that during your service you learned that any plan has to start with considering the situation. Defending your home isn't exactly the same as defending a battle position, but planning to defend your home is very similar to planning to defend a battle position. You start by examining your position (your home) and the surrounding terrain. You consider your resources (you, your wife). You consider the likely enemy avenues of approach (points of entry). You improve your battle position (good doors with good locks, locked windows, etc.). Consider what limitations you may have -- just as you wouldn't fire on adjacent units in the field you don't want to shoot up your neighbors at home. And most especially you consider your mission -- in home defense that mission is protecting your wife and yourself, not protecting your TV set or microwave, etc.

You wouldn't expect to defend your battle position the same way in a thick forest as in a desert. Home defense in an apartment is different from home defense in a detached home. Home defense in a single story home is different from home defense in a house with bedrooms upstairs.

Finally, let me emphasize that we are talking about defense, not patrolling. In home defense the best choice is almost always to take up a defensive position and let any intruders come to you rather than wandering around your house looking for them.

12 gauge pump double ought Buck. That's a good attention getter

You're asking the wrong question. It's not what kind of firearm, it's if the person weilding it is 100 percent, no doubt in their mind, can use it effectively. If not, it's more of a danger than an "intimidation factor". That advice was given to my mother years ago at a gun shop when she was considering home defense. She opted to move. And she was no wimp. She was a WWII Navy gunnery instructor (SBD Dauntless platform).

I agree with LTC Rodney Joye with some minor changes. For home defense, especially when your wife has limited practice with firearms, the best choice balances simplicity, reliability, and ease of use under stress. A 20-gauge pump-action shotgun, like the Mossberg 500 or Remington 870, is often ideal. Here's why:

Simplicity: Pump-actions are straightforward to operate—load, pump, aim, shoot. Minimal practice is needed to achieve basic proficiency compared to handguns, which require more training for accuracy and recoil management.

Effectiveness: A 20-gauge shotgun with #3 buckshot delivers significant stopping power with less recoil than a 12-gauge, making it more manageable for someone with limited experience. It’s highly effective at close range, typical for home defense scenarios. The Mossberg 500 or Remington 870 in 20-gauge, configured for tactical or home defense use, often has a fixed cylinder bore choke (no constriction) or no choke at all. This provides a wider shot spread (about 1 inch per yard) at close range (5–15 yards), ideal for home defense where precision is less critical.

Safety: Shotguns have less risk of over-penetration through walls compared to high-velocity rifle rounds (e.g., 5.56mm), reducing danger to others in the home. The spread of buckshot also makes precise aiming less critical under stress.

Intimidation: The sound of a pump-action shotgun being racked can deter intruders without firing a shot.