Haxe only has one compiler unlike most languages but, there is no reason to have multiple as the current one is all you need.
Downloading & Installing edit
The first thing you will want to do is download the automatic installer(you can also install it from sources or binaries if you are running linux) here, after that just run the installer and follow the instructions in the installer.
Once you are done open your command line program(cmd, terminal, etc) and enter "haxe" without the quotation marks. If it prints a list of commands then you are done installing, if you get an error message try uninstalling and install it again.
If haxe crashes on windows/mac uninstall the program as above but if that doesn't work check if your haxe is up to date with the library your are trying to install
Neko is not required but, it is a very helpful target.
You can download Neko here, just download the right version for your system and open the zip file with whatever you use and drag the Neko folder to be inside the same directory as your Haxe installation.
Setting-up libraries/targets for Haxe is easy, just open your command line tools and enter "haxelib setup" after that it will ask you a question about the directory, just press enter and your done!
Haxe has support for installing libraries and targets through your command line. Some of the most famous include C++, NME, and OpenFL.
Once you've setup(above), the way you install thing is just by opening your command line and entering:
haxelib install <name>
Just replace <name> with the name of whatever you want to install for example "hxcpp" which installs the c++ target. If you would like a list of all the targets and libraries you can install go here.