There are .22 handguns. I owned a Beretta .22 semi-automatic up until last Monday night, when it was stolen out of my automobile.
You don't mention whether you want a revolver or a semi-automatic pistol. Each has its advantages and disadvantages. Beretta has an excellent article on its website on Purchasing Your First Pistol at http://www.berettausa.com/communities/home_prot/feature.htm. You might want to read the article and then ask more questions. You also don't mention what you want to do with the handgun. If you want it for personal and home protection, you're going to want a different model than if you want it for competition.
Regardless, you are going to need to get some additional experience before making a definitive decision. To get experience, you might check with your local community college to see if they offer classes in firearms safety and use. If not, perhaps a local gun club will offer classes. In some states, a training program is required before a concealed-carry permit can be issued, and the local sheriff's department can steer you to the classes. You may also call your local police department and ask if you can sit in on their certification course or if they sponsor a course specifically for new gun owners. Once you have been briefed on range safety and technique, you may ask to try out a handgun you're interested in. Most gun owners will let you fire their handguns (although many--even most--won't lend their competition firearms and some police officers won't lend their service weapons--don't be offended if someone refuses) once or twice to get the "feel." Range owners sometimes have guns that you can try out as well.
My first handgun (nearly 30 years ago) was a Smith & Wesson Model 10 revolver. It had excellent balance and was very accurate. I won more than one trophy with it in competition. Since then, I've owned several revolvers and the aforementioned Beretta .22. I've also qualified with the local police department's officers using their service weapons (Glock 19).
All of this information may not be what you were looking for, but I hope it gives you a "feel" for the ins and outs of getting to know people and places that can help you gather more information.
P. S. I asked my husband, the certified firearms instructor of 30 years, what he recommends. He said the same thing: "What's it going to be used for?" Beyond that, he recommends a S&W Model 10 .38 Special revolver, which you can use for home defense once you learn how to use it, or a Ruger Mark III .22 semi-auto. Both types of ammo are easy to come by and the .22 is inexpensive.