This is a difficult question to answer without knowing what you intend to do with the weapon. That said...

Your first pistol should almost certainly be a .22, as it will be a great platform to teach you the basics of pistol shooting. Rounds are inexpensive, as are some of the higher quality pistols that are chambered for it. Roughly 80% of people shot with a pistol will survive, no matter what caliber is used against them. Shot placement is the key, which is rooted in basic marksmanship. The .22 is by far the best option to get you started on the right track.

HOWEVER-- it's not what I would recommend for a self-defense weapon. Many say that .380 is the bare bones minimum; I tend to argue in favor of 9mm. But that's an entirely different argument. Regardless of your chosen chambering, shot placement is the key.

For the casual shooter, or someone just looking for peace of mind, I recommend a revolver over any auto pistol. Despite the reliability of most semi-automatic handguns on the market today, malfunctions can and will occur, and without proper training/practice, they might cost you your life. A revolver eliminates the vast majority of these issues, and .38 is the most common and probably best suited to your needs.

Most people tend to go with something small, light and discreet. While there's nothing particularly wrong with this trend, unless you are going to be carrying it on a daily basis, Feather/Airweight pistols are NOT fun to shoot large volumes of ammo through. Again, for a casual shooter that plans to leave the gun in a nightstand, this isn't much of a worry. However, you do yourself a disservice by not practicing with a weapon that might some day be called upon to save your life. If you can't bring yourself to own something with a barrel longer than 2", I suggest you stay away from anything super light weight. Not only will it shave some cost off of your purchase, you actually stand to gain more than you lose in terms of recoil and accuracy.

Smith and Wesson makes a host of J framed (compact) revolvers in .38 chamberings, and are most often heralded as the "best". The Ruger SP101 is my favorite in this particular category, and has a great reputation as well. Taurus has improved the quality of their products in recent years, and are typically a bit more affordable than their rivals. The same can be said for Rossi, although personally, I would avoid giving one to anyone I cared about.

Again, I cannot stress enough the need for practice and training. You don't have to take a highspeed tactical class, but some sort of defensive pistol course is money well spent. That coupled with some range time will not only improve your abilities by leaps and bounds, it will give you the confidence to use your pistol if the time ever comes.