I was primarily thinking Xubuntu, but I'm open to other suggestions.
What I will use my home server for will be file hosting and running server software (Minecraft server, SRCDS, Fallout: NV MP Mod Server, etc.).
What's a good distro for this that has a GUI I can use? I don't like the difficulty if Ubuntu-server with its command-line only method.
ubuntu server is still the better option.
After installing, you just install the DE of your choice.
Any linux distro fits your requirements, and any desktop environment can run on any linux distro.
Nowadays, there's no difference between the Ubuntu Desktop and server except for the default installed packages. There used to be a ubuntu-server kernel a few years back. As Zoltan said, you can install Ubuntu server and then install a DE of your choice. However, I can't see any real benefit if you install Ubuntu server and then a DE. Once you install the DE you will have that whole desktop as if you were installing the standard Ubuntu, Xubunt, Kubuntu or Lubuntu. The fastest of all would be Lubuntu. If you've installed the server version already, you can just do "sudo apt-get install ${DE}-desktop" (replace ${DE} with the DE of your choice xubuntu, ubuntu, kubuntu or lubuntu).
Cheers