I'd so love to start a linux distro flamewar or even better a linux vs bsd disaster.
But the simple fact is that from looking at the course requirements is that any distro will suit your needs and quite possible any BSD variant.
That said, you probably need no heads-up aswell since this looks like a very simple course.
If you have ever seen a command prompt and a batch file, reading online the manpages of either "bash shell" or "C shell" will give you all the info you need on the scripting. This will also cover the part about running programs.
For the Xserver part of the course, who knows, there's so much to read about it.
Try reading some intro things at xfree.org.
The editors part is definitely emacs and maybe, just maybe, vi (if the lecturer is as hardcore as jenna jameson). No pun intended for the editor warriors, I love both editors.
System information commands. There's a whole section of the manpages on system commands, don't remember which number, check online. Even if you find it, there's so many of em and who knows what he'll show you in the actual class.
"UNIX Internet Commands". Still laughing on this one.
Hardly such a thing. Read manpages on telnet, ftp, ping, rsh and ssh.
Simple dos experience is the same.
Other commands to look at manpages off the top of my head:
tar, gzip, grep, regexp (prolly not), ls, find, locate, more, cat, awk (probably not).
Finally, you don't really need to bother installing linux if the course is your only concern. Installing cygwin will give you the command prompt and xserver to satisfy all of your practice curiosities.
Waaaait a minute...
What on earth am I saying? proposing NOT to install linux?
Get slackware and die of starvation while you try to manually configure X.
NOW GO!