Personally, I'd go with an option #4. Buy the 22 caliber pistol first. Learn the basics of shooting. Learn how to safely care for the use of your weapon. 22's are a great way to start. As you mentioned, they are inexpensive to own and shoot. You can easily find a 22 pistol; either semi or revolver for around $200 or less. Once you are comfortable shooting; comfortable cleaning and caring for the weapon, and comfortable with guns in general; then you can move on.
When the time comes to get the 2nd weapon for home defense, I personally recommend a quality revolver. I recommend a 357 magnum such as a Smith&Wesson. You can shoot 38 specials in it (Which aren't that expensive, and they are easily available). Then you can move up to 38spl +P that are hotter. Then move up to 357 magnum. Or settle anywhere in between. For inexperienced shooters, the revolvers are the best option for a home defense gun. It's simply "Point and Click". Semi-autos can become complicated. Not so much in their use, but in their cleaning and most importantly; when something goes wrong. I am not dogging anyone who has a semi-auto for self or home defense. But unfortunately the time will come for the person who isn't very experienced in using their weapon when they are going to need it. Their heart is going to be racing. Their adrenaline is going to be pumping. Their brain is going to be think every possible thing. And the semi-auto is not going to work for them. They'll either have forgotten to put a round in the chamber; or forgotten to take the safety off; or if they do chamber a round, it may not seat properly; and the list goes on. And then they are going to possibly get hurt; or worse yet killed. For the experienced shooter, this can sometimes still be a problem. All the practice in the world can't prepare you for a real life scenario of someone you are confronting with your gun. My "PRIMARY" weapon at home is either my S&W Model 13 357 magnum and/or Remington 870 shotgun. Both are pretty much point and click and almost idiot proof.
I purposely train with semi-autos loaded with a mixture of live and dummy loads. I practice rapid shooting. And when the dummy load misfires, I have to jack the next round in manually. I practice this in a timed situation and having to hit my target. If it's a miss, then that's as good as not shooting. I've been shooting for more than 30 years. 20 of those years I've had the benefit of uncle Sam training me and allowing me to practice. On and off duty. But this is not saying you should or shouldn't get a semi-auto. It's to say that there is a time for every purpose under heaven. And for the new person shooting, in my opinion you should have a revolver for home defense.
So I suggest getting a 22 pistol. A semi-auto like a ruger is a good choice. You can learn about gun safety, use, and semi-autos. Then when you think you're ready, spend some wise money on a quality S&W or Ruger revolver. If you get the "BUG" for guns, like many people do; you can eventually buy a semi-auto. And like many of us, by the time life has gone by, you will probably have 3-4 hand guns; 2-3 rifles; a couple of shotguns; a few 22's; and so on. But in the beginning, it should be a 22lr for learning, then a revolver for home defense. But hell, that's just my opinion.