Since Internet was born on Unix machines, you find plenty of nice and easy-to-use applications under Linux. Here are just some:
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" user@somewhere < msg.txt. You may like programs like
xmail or some such.
tin, very intuitive and self-explanatory.
ftp, ask your
sysadm to install a graphical ftp client like xftp.
netscape, or xmosaic, chimera
and arena are graphical web browsers; a character-based one is
lynx, quick and effective.