I don't think you need a virus checker with linux. Not operating as root is an automatic protection you don't get with windows. You should have a good firewall, though. Seawall is a good ipchains-based firewall for Red Hat. http://seawall.sourceforge.net
If you have Pine, while viewing the message, press 'h' to show all the headers. Reading from the bottom of the headers you can see the machine that the message originated on and compare it to the supposed sender. Good for the latest worm going around. Reading from the bottom, compare the last "From" name and IP to the last "Received" name and IP. If it's okay, they'll match. With some like yahoo, at least the IP servers will match.
Chkrootkit is a great idea in any event.