Wow. Such a big area to cover.
Well, there are three basic kinds of handguns: Revolvers, Semi-autos, and Single-Shot. Yes, I know that there are some others such as two-shot Derringers, but those are the main three.

OK, starting with the oldest and most basic type: the single-shot pistol.
[as an aside, i use the terms "pistol" and "handgun" interchangeably and I include revolvers in this group]

The single-shot pistol only carries ammunition for one shot at a time. After shooting it, the pistol must be reloaded. Modern single-shot pistols are mainly used for hunting or competition target shooting such as in The Olympics. They use modern ammunition and they are easy and fast to reload. They can be chambered for just about any pistol and most rifle cartridges and can be extremely accurate.

Let's continue with revolvers.

Back in the 1830s almost all firearms were of the single-shot variety. There were a few double-barrelled guns and a few that used more than two barrels. The majority were of the "shoot it once and then reload it" kind. About this time one Samuel Colt had a great idea that became the revolver as we know it. Until the mid-1860s it was, for the most part, still loaded with loose powder and round lead balls. The "modern age" of the revolver began in 1873 with the introduction of the Colt Single-Action Army Revolver. This is the revolver made famous in so many Western movies (even on movies set before 1873 -- go figure). The Colt Single-Action Army (SAA) used the then-new self-contained brass cartridges, though they still used the old blackpowder. One step at a time.
Varieties of this revolver are still made today. You must cock the hammer back before each shot. There is no safety mechanism that prevents the gun from firing, nor is any needed.

The next big development in the world of the revolver was the Double-Action mechanism that allowed the revolver to be fired with only a (long) pull of the trigger. Pulling the trigger both cocked the hammer and rotated a new chamber into alignment with the barrel before allowing the hammer to fall firing the weapon. Hence the "Double-Action" name. Almost all Double-Action revolvers could be fired as a Single-Action revolver if so desired.

That pretty well gets us up to the present day in terms of revolver technology. Revolvers are still viable firearms and they can usually be chambered for higher-powered cartridges than are available in Semi-Autos.

Did I say "Semi-Autos" in that last paragraph?
Well that's what's next. Handguns that automatically reload themselves after firing a shot. In the firearms world these are called "self-loading" pistols or "semi-automatic" pistols. The term "automatic" as applied to firearms almost always means that the arm in question is capable of firing more than one shot with each pull of the trigger. These are real machine guns. That's not a problem. Machine guns can be fun to shoot, but that's not what I am discussing right now.

Arms designers long suspected that the energy released when a firearm was fired could be used to prepare the gun for firing the next shot. That should speed up the process of firing multiple shots and was seen as desirable.
Most of the early work in this area was done by the Germans. The first truly practical semi-automatic pistol was introduced in 1896 by Paul Mauser. There were earlier semi-autos but none of them were very practical. The model C-96 Mauser pistol quickly gathered the nickname "Broomhandle" due to the shape of the grip.

This C-96 Mauser from my collection was made in 1914. Photo by author

The C-96 fired a .30 calibre (7.63mm) bottlenecked cartridge that was very high-powered for the day. This pistol gathered a lot of admirers and users, including one Winston Churchill. It holds 10 rounds of ammunition in the magazine and reloads quickly if the proper stripper clips are used.

Photo by author

At the same time in another part of Germany another fellow was improving on the earlier Bergmann-Bayard pistol. By 1900 he had it pretty well worked out. Georg Luger's design looked something like this:

This is a 1970s-era Luger made by Mauser with the 6-inch barrel. From my own collection. Photo by author

Herr Luger had succeeded in making the semi-automatic pistol convenient to carry and reload. Like almost all modern semi-autos it loads via a removable magazine housed within the grip of the pistol. By 1908 Herr Luger -- at the request of the German Army -- had developed for his pistol the 9mm Parabellum cartridge which is still one of the most popular in use today. The pistol held eight rounds in its magazine.

About this same time a fellow out in Utah by the name of John M. Browning was working on his own designs. Those designs culminated in 1911 with the Colt Government Model pistol which is almost always just called "the 1911" -- at least by Americans. This was a very effective and practical pistol indeed. It fired the big ".45 Automatic Colt Pistol" cartridge -- usually stated as the .45 ACP -- and it held 7 rounds in its magazine.

Image from the internet. I owned one once. It didn't feel right in my hand and the sights were tiny. I traded it for a Browning High-Power (aka: P-35).

That pretty much brings us up to the present barring an awful lot of plastic-framed guns and Double-Action-Only guns which have very long and heavy trigger pulls for the most part.

What handguns do I have and like? Well, the Mauser C-96 and the Luger above are both among my favourites, though not particularly practical for home defense or daily (concealed) carry. My choice for these purposes is usually a CZ-75 or a clone from the Italian maker Tanfoglio.

Here's a brief list of some of my favourites. Links will be added as the pages are written.
        Colt 2nd model Dragoon
        Mauser C-96
        Ruger Blackhawk
        CZ-75 and clones
        Mitchell Citation II (a clone of the old Hi-Standard Citation)
        Star Megastar
        Browning P-35 (aka: "Hi-Power")
        Taurus PT-92 (close clone of the Beretta model 92)

A brief note about 1911s and Glocks. I have owned both. They just weren't "right" for me. The 1911 was uncomfortable and difficult for me to shoot accurately. The Glock 27 was a very reliable gun; it was very accurate; I shot it very well -- but it just didn't "feel right" to me. Both the trigger and the plastic frame just didn't "work" for me. Other folks love them. I won't say anything against them. There are plenty of other people who write in praise of 1911s and Glocks; I shall leave that to them.