Bud,
You've come to the right place. There will be a lot of opinions thrown at you but they will all agree that the .22 is not a self-defense round.
There are only two ways that bullets stop aggressors (or game animals). One immediate way is by disrupting the nervous system by a head or spine shot and the slower way is by exanguination (bleeding out to a point of incapacity)
On TV, one or two shots to the chest of the bad guy stops them immediately. In real life a handgun shot to the heart will not incapacitate an aggressor for at least 15-30 seconds, maybe shorter if it is a 357 mag, 44 mag, or 45 ACP. Most real-life combat shots are not to the heart. So unless you have an effective head shot or spine shot you will be dealing with an aggressor who has been shot and is now Really Angry. In a confrontation such as that you want to be able to throw a lot of lead in a short period of time, which suggests a reliable semi-auto rather than a revolver. In a home-invasion scenario, I consider my pistol as something that will buy me time to get to my 870 Remington Express shotgun.
I personally think that, unless you are well trained in combat, nothing smaller than the .40 S&W (that's the name of the cartridge, not the gun, you may buy a Sig Sauer pistol that will say .40 S&W on the side) should be considered as a Self Defense (SD) round. And even most our our well-trained combat troops really would rather have a .45 sidearm rather than the 9 mm which they are issued.
Fortunately, S&W has a gun for you. It is the .40 cal SD. Or, if you want the most popular police issue in the US, it is the .40 cal M&P. They also make a 9 mm SD and M&P which many posters will argue is adequate for self-defense. That's a debate with no end. The .45 cal M&P is also a great gun but the price of ammunition may keep you from practicing with it.
If money is tight, the S&W Sigma .40 is a lot of gun for the money and you can often get one for about $300. The SD .40 can be had for about $400 and the M&P for about $500. These are sale prices, add about $50 if not on sale.
My suggestion is that you find a range that will rent several guns to you so you can "test drive" them. With ammunition expect to spend about $100. But I suggest that you take a firearms safety course first. Most ranges offer these and they are well worth the money.
For a fun gun that is cheap to fire, but not cheap to acquire, the 617 is a great gun, it's a classic. But if you shoot someone with it, you're just gonna make 'em mad.