I have 1 desktop computer (terrible specs) and 2 laptops (decent specs).

I use my desktop as a server (Windows XP). It provides my other two laptops (both originally Windows 7) with a network printer and a network 1TiB external hard drive. Both network devices need to authentication to access. Both laptops log into the same main user (there's only one user) within the desktop to access those devices.

I want to ditch this Windows setup for a Linux setup, but am unsure about how to begin, what software to use (SSH, FTP, or some Windows share alternative for linux) and what the end result should look like.

I've installed Fedora 16 on this laptop, and Ubuntu Natty Narwhal on the other laptop. I've configured both of them to connect my Windows-shared external hard drive. The only thing I want to do now is rid my desktop of Windows XP and install some linux distro.

First of all, what distro is best suited for a computer which will primarily be used for providing other computers with external disk space and a printer over the network, needs to be configurable over the network and has no monitor?

And second of all, what do I need to do to achieve such a setup?

Thanks in advance!

All this is already included, if you install some distri on the machine.

For all shared directories use samba server on the desktop pc and samba client for the clients.
The printer is shared via CUPS (CommenUnixPrintingSystem ) which can offer it's services over the net.

In order to configure the machine I would recommend to use SSH server.
But this needs knowledge in cli programms.

But you can share a GUI as well.
A vnc server on the desktop machine and a vnc viewer on the client side is enough.

All distris can handle this.