First, a gun is NOT a magical talisman, and it can be quite difficult to use effectively in a stressful situation.
Second, get training.
Now, onto your questions. There are two major categories of handguns, pistols and revolvers.
For self defense revolvers, the smallest applicable chambering is 32 H&R mag, but that isn't very common, and is somewhat marginal. For the most part, it starts with 38 special and the goes up to 357 magnum. Here's the best part, IF you get a 357 magnum, you can shoot 38 specials with it is well. This means lower cost practice ammo and less kick.
For self defense pistols, the 'floor' is the 380 ACP, which is also called the 9mm short, aka 9x17mm (9mm diameter projectile 17mm long case.) The 'normal' 9mm, aka 9mm luger aka 9x19mm is a significant step up in power. A step up from that would be the 40 S&W, but these tend to hold a few less cartridges in the gun. A step up from the 40 S&W would be the .45 ACP, and again, you have less shots in the gun. Kick goes up with each of these.
Now, let me tell you something about guns that novices often don't realize right away.
SMALL GUNS KICK HARDER THAN BIG GUNS. Most people tend to be tuned in to the emotional part of their brain, not the logical part, when handling guns or shopping for guns for the first time. But as a man of science, I am sure you can see that a gun's power comes from the gunpowder in the cartridge, not the actual gun. A gun simply directs a controlled explosion, and if you are going to have a controlled explosion in your hand, the more steel wrapped around it, the better!
The flip side of this is
BIG GUNS FEEL LIKE BOAT ANCHORS IF YOU CARRY AROUND ALL DAY.
Taking that all into account, here's what I would suggest. And as a doctor, I am going to make the false assumption you have oodles of cash lying about your home.
Get 3 guns.
Get a .22LR revolver for practice, something like these two. It is the gun you will learn on.
http://www.thegunsource.com/store/item/7802_Hand_Guns_Pistols_Ruger_Ruger__New_Bearcat__Singl.aspx
http://www.thegunsource.com/store/item/9924_Hand_Guns_Pistols_Taurus_Taurus_Firearms_94_Small_.aspx
Second, get a medium frame .357 revolver with a 4 to 6 inch barrel and adjustable sights. If you can, get stainless it will withstand your sweat better.
http://www.thegunsource.com/store/item/7849_Hand_Guns_Pistols_Ruger_Ruger_GP_100__Double-Acti.aspx
http://www.thegunsource.com/store/item/7851_Hand_Guns_Pistols_Ruger_Ruger_GP_100__Double-Acti.aspx
http://www.thegunsource.com/store/i...s_Smith__Wesson_Smith__Wesson_686_Plus_R.aspx
http://www.thegunsource.com/store/i...s_Smith__Wesson_Smith__Wesson_Model_686_.aspx
Third, get yourself a small, light, snub nose handgun. This will be a real kick in the hands to shoot, but will be a joy to carry. Rely on .22LR for learning the basics, and the medium frame gun for truly potent shooting, as well as a home defense gun. Only shoot the little light gun just enough to get familiar with it, and then carry it. It would probably be better to carry the medium framed gun, but the truth is, most people don't because it is too heavy. You'd buy this light little snub nose after about 2 months of carrying the heavy medium frame gun around anyways.
http://www.thegunsource.com/store/i...s_Smith__Wesson_Smith__Wesson_329_Centen.aspx
http://www.thegunsource.com/store/i...s_Smith__Wesson_Smith__Wesson_MP_340_Rev.aspx
http://www.thegunsource.com/store/i...s_Smith__Wesson_Smith__Wesson_638_Airwei.aspx
http://www.thegunsource.com/store/i...s_Smith__Wesson_Smith__Wesson_642_Airwei.aspx
Note, many of these revolvers use titanium, scandium, or other specialty metals to stay quite light. Also, most don't have the hammer exposed, one less thing to snag on your pocket when you draw.
Get yourself a Gunvault
http://www.gunvault.com/ for home storage. It won't stop a theif with a good crowbar and 30 minutes to spare, but it will keep the gun from smash and grab types, as well as out of the hands of children
Invest in a good belt and holster for your snubnose. There are many different types, but that is a quesion for another time.
I recommend the revolver for a beginner because it is such a versatile gun, it is intrinsically easy to understand, it is easy to see if it is loaded or unload, and it stands up to benign neglect better than anything else. No gun should ride around in a lint filled coat pocket for weeks on end, but the revolver seems to hold up better than semi autos in this regard.