The internet should "just work". Try powering the computer on with the ethernet cable plugged in. Open up a terminal (Applications>Accessories>terminal) and type the command "lspci" without the quotes. This should tell you what ethernet hardware you have and whether Ubuntu is having a hard time. type the command "dmesg" which outputs information about the boot process. Look for errors here. Lastly, congratulations for trying Linux but more importantly welcome to the Linux community! Don't be shy. Hop on irc and ask around http://www.ubuntu.com/support/community/... http://www.ubuntu.com/support/CommunityS.... There may also be a Linux User Group (LUG) in your area.
I'm liking the idea of setting it up as a stationary media player. I never really considered it's function if it was constantly plugged in. I'm wishing it had video out now! Some thoughts for what I can do:
1. clock/alarm clock
2. audio media center (on the SD or streaming or pandora)
3. some weather app (kind of like a chumby) I'll update here if I can find the apps to do these.