"So, my questions, in a nutshell, does RedHat have free, open-source server software that I can download and install?"
But CentOS is a clone of RedHat and is free.
There is also Fedora, which is free, and is the RedHat development branch (sorta), but maybe a little too bleeding-edge.
Finally, I recommend Ubuntu Server Edition, which is free.
However, there is a lot more to this than just the "free download" part. For example, what is the "networking project"?
- For a web server, you will need to make sure you install Web Server software, such as Apache. Others include nginx and lighttpd, but Apache is probably the best place to start.
- For a database server, you will need to install database server software, such as MySQL. Other options include PostgreSQL, and some others, but those are probably the biggest two in the open source world.
- For other projects, you will need other server software.
But my point is really this: you do not need to install an OS with which you are unfamiliar, as all you can find all of these or their equivalents that will run on Windows, too (or Mac OS X for that matter). (And this is coming from a die hard Linux fan who doesn't use Windows at all.) Apache? Runs on Windows. MySQL? Runs on Windows.
Just something to consider.
Also, about the Linux distros. While Redhat, CentOS, and Ubuntu do have "server versions" of their OSes available, in the Linux world, the distinction between "server" and "desktop" is really one of packaging than something fundamental. Take Ubuntu server vs Ubuntu desktop, as an example. You can start with either, and have a full fledged Apache web server running. The end result will be the same. Whereas, in Windows Server, there are some fundamental differences between server and desktop versions of the OS. (But those differences probably revolve primarily around licensing. Anyway, I digress.)