Cliff's Notes version:
If you're inexperienced w/ handguns, I'd suggest a full size (4-6" barrel), steel frame, 6 shot (or more) revolver w/ fixed sights chambered in 357 Mag. Start off shooting mild 38 Special rounds, advancing to +P 38 Spec loads when you can handle them. Advance to full 357 Mag loads ONLY once you've mastered the +P 38 Spec loads. If you can't make it to 357 Mag loads, just stay w/ the +P 38 Spec loads, which are still very formidable self defense rounds. A similar sized gun in 38 Special w/ +P rounds is good too if you don't have any interest in the recoil/muzzle blast of the 357 Mag.
If you'd rather have a semi-auto, I'd suggest a full size 9mm from a reputable manufacturer, e.g. S&W (M&P series), Springfield Armory (XD series), Ruger (SR series), Glock, Sig, CZ or Beretta. I prefer DAO, striker-fired or SAO, but you may well prefer a SA/DA type. Likewise, I mostly prefer no external safeties, but you may want a safety. If you're experienced and comfortable w/ the platform, a reliable 1911 is a good choice, as well. Try to handle, and shoot, a number of semi-autos before deciding which one to buy. Some of the bigger cities have shooting ranges that will let you rent a handgun and shoot for a period of time. If your wife or kids will be handling the gun, be sure they can rack the slide and manipulate the controls on a semi-auto.
For home use, the best self defense weapon is not a handgun, but a shotgun, usually a 12 gauge, but 20 gauge is a good choice, as well. A youth model is a good idea if someone of small stature may use the gun. A pump Mossberg or Remington is not expensive, as long as you don't get a bunch of "tactical" stuff on it.
Full Version:For a self defense gun that is NOT going to be used in concealed carry, you don't want, nor need, a compact or subcompact gun; get a full size gun. All things being equal, a smaller and lighter gun is generally more difficult to shoot well than is a larger and heavier gun, especially for newbies. Personally, I think revolvers are easier for most newbies to learn w/ than are semi-autos. OTOH, some newbies start out w/ semi-autos w/o any problems. No one but you will know which which category you'll fall in to.
The best self defense calibers are 9mm, 357 Mag, 357 Sig, 40 S&W and 45 ACP; the 38 Special also has a good track record, but not like the above.
The semi-auto vs revolver debate always generates a lot of interest. Ruger, Colt, Chiappa and Smith & Wesson are top notch makers of revolvers; other makers that seem to have spotty quality control include Charter Arms, Rossi and Taurus.
Depending on your inexperience, formal training in handgun handling and safety may be indicated.
If you can swing it, I'd strongly consider buying a 22 LR to learn the basics of handgun handling and to practice w/. If you want a revolver for self defense, make the 22 LR a revolver; if the SD gun is a semi auto, get a semi auto 22 LR.
Last, I'm expecting for a recommendation (and debate to follow) for the Judge to pop up soon. Personally, I think there are a lot of guns other than the Judge that have a proven that have a proven track record as a fight stopper.
Good luck. Let us know what you buy and be sure and include PICS. :-)