If you're only loading up *nix for the sole purpose of a Minecraft server, go all the way and use a distro that was meant for servers. I'd go with CentOS or even MineOS CRUX, which is kind of at the far end of the spectrum because it has been designed solely for hosting minecraft. MineOS is so lean and mean, I got amazing performance just off a virtual machine on my windows laptop. :-D
“Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.” — Albert Einstein
"Never try to teach a pig to sing; it wastes your time and it annoys the pig." — Robert Heinlein
It is basically Ubuntu, but more stable, lighter on resources and it is compatible with nearly all hardware out of the box. I used to use Ubuntu (was forced too) and it is a messy OS that is based off Debian unstable.
Three mentioned; Ubuntu Server, Debian and CentOS are all great choices. Ubuntu has a lot more "stuff" in it, so if you are looking for something semi-lightweight for a VPS I would recommend Debian. It's package management is top notch and it will run fine. CentOS is also a good operating system for explicit serving, if you are looking at running LAMP stack on your server, it is also my recommendation. Most other distributions will sink in quality a bit or be too difficult for a simple server even though they may offer maximum customization (Arch, Gentoo).