Most distributions will have an option to select which packages to install, there you should deselect the entire X Windows system, all X applications, and desktop environments like KDE and Gnome. Preferably install only the base system and things like documentation, man pages, networking, and development packages.
I would really recommend slackware linux or FreeBSD here, they are very close to the original unix standards.
If you want something easier to install, Vector Linux 4.3 standard edition will be a good choice (
www.vectorlinux.com). It gives you the choice of excluding X-Windows.
Damn Small Linux is a bootable cd but it can be installed too, good choice if you want a GUI to work in too.
Your LAN card may or may not be automatically configured (depends on which distro, and what lan card you use), but you can get the drivers from its manufacturers site.