Since Internet was born on UNIX machines, you find plenty of nice and easy-to-use applications under Linux. Here are just some:
Mail: use elm or pine to handle your email; both programs have on-line help. For short messages, you could use mail, as in mail -s "hello mate" [email protected] < msg.txt. You may like programs like xmail or some such.
Newsgroups: use tin or slrn, both very intuitive and self-explanatory.
ftp: apart from the usual character-based ftp, ask your sysadm to install the full-screen ncftp or a graphical ftp client like xftp.
WWW: the ubiquitous netscape, or xmosaic, chimera, and arena are graphical web browsers; a character-based one is lynx, quick and effective.