In your case, the only thing you need is a simple and stable kernal and basic applications without X. If you need a GUI interface, go with fluxbox or blackbox. All really good, efficient, stable, GUI interfaces.
EDIT:
Forgot you needed applications. Imho, it depends on what skill levels you have with running linux. If you're a complete newb, then run Ubuntu; if your skills are sufficient, then I'd advise running gentoo or fedora. Mind you, the less unstable the distro is, the more of a pain-in-the-ass it is too; but often is much more demanding--and rewarding ;)
EDIT:
Forgot you needed applications. Imho, it depends on what skill levels you have with running linux. If you're a complete newb, then run Ubuntu; if your skills are sufficient, then I'd advise running gentoo or fedora. Mind you, the less unstable the distro is, the more of a pain-in-the-ass it is too; but often is much more demanding--and rewarding ;)
Do what thou wilt shall be the whole of the Law. Love is the law, love under will.
.::The Rights of Man::.
.::The Rights of Man::.