I know this isn’t what what the OP had in mind, but it’s .22 and kinda cool so . . . Calico M-100. Sample pic.
Since your new to shooting firearms, a .22 is a good place to start. As far as self-defense is concern, they ARE lethal. Pistol cartridges are not generally considered “man-stoppers” (ie instantly ending a physical threat) that a rifle cartridge or shotgun slug could be, unless you manage to disrupt the brain stem or sever the upper spine. You always have the option of putting several rounds (3, 4, 5?) into your attacker. More holes = quicker blood loss. Many people practice double-tapping (firing two rounds as ACCURATELY and quickly as possible). Practice firing two rounds center mass at single targets and at side-by-side targets. Left-then-right, right-then-left, strong hand (right hand if you’re right handed), and weak hand (left hand if you’re right handed). Practice triple and quadruple tapping as well.
Being able to actually hit your attacker with your firearm of choice is very important. Putting one round thru the coffee pot and another into the sofa isn’t going to stop a crazed, drugged, knife-wielding attacker. (How far could you walk in 30 seconds and still be able to repeatedly thrust a knife into a large, tough pot roast?)
Remember, before you resort to any lethal self-defense, you need to believe that your life or someone else’s life is in IMMINENT DANGER. You must believe that your life is in danger NOW. Not five minutes ago or 10 minutes from now but right now or a State Attorney may decide to make an example of you. If there is a closed door between you and your attacker, you are not in IMMINENT DANGER. If they are firing thru the door, then do whatever you think is best to save your life.
Some minor pistol calibers would be .30 Carbine, .32 S&W Long, .32 Magnum, .380 Auto, 9 mm Mararov, 9 mm Luger, .38 Super, .38 Special, .38 Special +P, etc.
Some major pistol calibers would be .357 Magnum, .40 S&W, 10 mm, .41 Magnum, 44 Special, .44 Magnum, .45 ACP, .45 Auto Rim, and .45 Colt, etc. Major pistol calibers can have quite a kick (recoil) and muzzle flash. Work your way up to the .44 Magnum and .454 Casull-type rounds.
And heavier pistols/revolvers are easier to physically shoot but more difficult to carry.
Another consideration is whether you want a semi-automatic pistol or a revolver. If you’re thinking of eventually going larger, that might influence your initial choice of .22. Or buy/rent a .22 revolver and pistol and see which style you prefer.
I have one of these. Fun to shoot but not very easy to conceal!
Bummer. Doesn’t look like I can get there from here.
They are discontinued now.
Get this and fuhgedabout magazine extensions
Generally speaking: .357 has been reliably shown to be the better “man-stopper” (bette rpenetration, better temporary and permanent wound cavities) than .45, .40, or 9mm. And as other have pointed out, a .357 revolver will readily take the cheaper .38 Special for range time, though I do recommend regularly putting some .357 though it, too, just so you know what you’re dealing with. The same gun will shoot differently from .38SP to .357.
And also as others have pointed out, .22LR has been scarce on the ground lately, while I’ve had no problem picking up .38 for range time with my Ruger GP100.
Having said that, a .22LR is a good place for a beginner shooter to start to get into good shooting habits, and the various offerings of handguns with changeable barrels lets you get a two-fer. Going to a shooting range that has rentals also lets you try various guns before you buy one.
Watch this, then all this guy’s YTs. He’s very knowledgable about firearms.
Actually, the .22 is used to kill - by assassins. The bullet is fired into an eye socket of a bound victem.
Its sole benefit is that it is a sub-sonic round, and easier to muzzle.
Another vote for 9mm minimum
Yeah, this is what I was thinking of + I have a single shot Contender in .45 / 410.
Inside a house, heavier 410 shot weights would be a pretty stiff walk to take with several loads from a shooter at 20’ & under.
Might not kill the kid down the block with it either.
Luckily I don’t have to worry due to my local terrain I can use a Wart Hog Gatling gun in 20MM or .50 mounted on a swivel if I want. 
YMMV
I had a whole spiel ready but, that’s just not fair.
Depends on your inclination and your needs. If you’re handy with a Ruger 10/22, it’s all you’ll need, unless you live in Somalia. A prone shooter armed with a semi-auto is hard to take down, even by several gunmen armed with handguns.
Wait a minute, did you steal OP’s wife? 
Huh. I missed that. I don’t think disposing of evidence really falls in the ‘lost’ category though. 
Also consider as part of your home defense quiver a tactical flashlight. I have a 500 lumen hand held flashlight. Momentarily confuse and blind the intruder with a steady beam from the light and give yourself a few extra seconds to decide on your next course of action. And have a plan depending upon how and where the intruder enters…of course none of this is relevant if the intruder has the drop on you!!
My 2 cents… A .38 or .38 Special in DA. (double action) The .38 Sp. with hollow point rounds has a lot of knock down power.
A double action pistol removes having to remember if the safety is off/on or if you’ve chambered a round. Squeeze the trigger, the weapon fires.
The only drawback to a ‘wheel gun’, IMO, is you’re limited to 5 (or 6, depending on the model) rounds to get the job done. The remedy to this is practice, practice, practice!
YMMV 
No, and no. A .22 doesn’t go ricocheting around the body. If it had the energy to penetrate tissue after bouncing off tissue, it would have penetrated that tissue.
The ability of a handgun bullet’s ability to damage tissue through it’s temporary cavity is greatly overblown. The only significant wounding mechanism you’re looking at with a handgun bullet is the physical hole made by the bullet.
As for the OP, if you were to go with a .22LR for self defense, I’d recommend a .22 revolver. Too many times with .22s I’ve had them misfire. With a semi-auto, it’s a clearance drill. With a revolver, you just pull the trigger again. I’ve not fired one, but I’ve liked the feel of a Ruger LCR I handled at a gun store.
Rimfire cartridges are a poor choice for self defense before we even address the caliber. Even a .22 magnum is a poor choice.
If you want a small caliber, go with 9mm or .38 special. .380 autos are palm slappers, and the newest round of nano 9mm are just as difficult to shoot.
I’d go with a Ruger SP101 in .357 in order to shoot either that or .38 special. It is a five shot revolver, and you can load all five because it uses a transfer bar. The all steel gun has enough heft to soak up recoil.
…and you should always assume the intruder has a drop on you.
If you’re in your bedroom, and you think someone has broken into your house, you should only clear your house if you *absolutely *must do it (e.g. children sleeping downstairs or whatever). The best strategy is to stay put, and let the intruder come to you.
Agreed! 
For another informative gun site check this out. The site has a lot of different videos using fairly methodical methods to test penetration power and accuracy of various types of weapons and the different rounds available for the weapon.
Yep, that’s a good one too. I had a link to that site on my old computer but had not checked it in a while. Glad to see they are still at it.