Preface
To start off this post, I want to explain what a keyboard layout is to those that might not be the most computer literate, and simply just select English US/Canada/GB/&c on their operating system when installing Windows, Mac, Linux, BSD or what-have-you and leave it at that; never thinking about where a key on their keyboard is or is supposed to go.
QWERTY
The best place to start when it comes to alternative layouts to QWERTY is QWERTY itself. One has to know why QWERTY is bad before one decides they want to switch it, because if you have never used a better alternative, you will not know why what you use is bad.
DVOŘAK
(Yes, I know they layout and creator didn't use Ř in their names)
Others
There are many, many more modern layouts for English than simply QWERTY, DVOŘAK or Colemak. Some of the other prominent ones that come to mind are Norman, Workman and the Carpalx layouts.
My biggest recommendation would be to stick to a modern alternative, as the software and information used to create these are much better than much older alternative layouts—such as DVOŘAK. The reason being that you will find, when put to the test, older layouts such as DVOŘAK, are better than QWERTY, but still much worse than their modern competition. As for which one to choose, in most cases the difference is really minimal, and so any will do.
You want to look for the design philosophy the creator used to make the layout, and whether or not that is the most comfortable to you, and comfort really is king when it comes to this, not speed. Most people going into this will think that an alternative layout will achieve better speeds, but that is not and never the goal of using another layout. You can definitely achieve very high typing speeds on QWERTY, and many have. The key in using an alternative layout is ergonomic, and thus that should be your primary objective when looking to learn an alternative layout.
A good secondary objective might be how supported it is by default on any major operating system you plan to use, as not everyone will let you install stuff onto their computers if you ever have to use it. The three major operating systems—Windows, MacOS and Linux—all support QWERTY of course, as well as DVORAK and Colemak. Linux supports a couple more like Workman, Norman and if you use FCITX, a few other. It has been many years since I have used Windows (about 10 or so), so I do not know which, if any, other alternative layouts they support natively.
Colemak
Colemak-DH
To get this out of the way, most consider Colemak-DH to be an upgrade to the baseline Colemak layout; I am not one of those people. Colemak-DH, as its name suggests, moves the D and H keys away from the home-row and into the bottom row so that you curl your hands down rather than extend them to the centre keys on the keyboard.
Many people dislike this extension of the fingers and prefer to curl them down, thus feel that Colemak-DH is more comfortable than the standard Colemak layout. I, on the other hand, feel the opposite: curling my fingers down is more uncomfortable than extending them on the home-row. So for those new to Colemak or those that are on the fence which one to learn, maybe confused at which one is more « correct » or « better » , then I recommend trying them both and figure out if you prefer curling your fingers down or extending them on the home-row; that will be your answer which one you should commit to and learn.
Colemak (Standard)
Sites for practising or learning new layouts
KeyBR is really good for initially picking up a layout.
MonkeyType is a general typing tool that allows you to see your words-per-minute, and set other settings for typing. I recommend, for MonkeyType, to reset on errors, as typing 150WPM does not really matter if you are typing half of the words incorrectly.
Conclusions
For me personally, I have been through many alternative layouts. I have landed on, and stuck with, Colemak's base layout.
As for anyone reading this, my conclusion is that your goal should be ergonomics, and not speed. If you only want speed, stick to QWERTY, you can achieve very high speeds with it if you actually learn to type correctly. Otherwise, if you are looking for more comfort and a better ergonomic typing experience, then look for modern alternative layouts, especially those that are supported by all the main operating systems if you plan to use others' computers; if not, then you should branch out to and find the best keyboard layout that fits your typing style.