Agree with BT, what you are describing most Linux distros can handle with little problem. What you will want to look into is Samba, which I believe Ubuntu comes with by default(Though I am not sure). Samba will allow you to provide network shares to the other computers on your network, wether they be Linux, BSD, Mac, or Windows via the SMB protocol.
Samba can be tricky to set up correctly though, so make sure you ask when you need help, but please GOOGLE first
Especially with Ubuntu on their ubuntuguide.org (Right Address someone?) site I am sure they probably ahve a guide.
As you get more comfortable with linux you can create much more lean installs to run as a server that may work even better for you via Gentoo, however I dont reccomend it at first myself