- internet connection sharing
- DHCP server
- Freenet (Sun Java)
- SSH server
- Take up as little RAM as possible.
- Must be 100% usable in console (remotely over ssh).
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Do yourself a favor and pick a distro with an active support community such as Fedora or Ubuntu. For some one with little experience (or a lot) it can be an invaluable tool. Most likely someone else has had your same (or a similar) problem. With Fedora I regularly use sites such as fedoraforum.org and stackexchange sites (of course).
They all can perform those functions for the most part, but something like Fedora is always easy to recommend.