Inherently Linux is more secure than Windows due to the structure of the system
There is no need for antivirus as there are no Linux viruses in the wild at this time.
Create secure passwords for both root (especially for Root ) and for the normal user account.
A secure password should have letters ( abcdef...ect) both upper case and lower case as well as numbers and symbols ( 1234...#&$@ )
stay away from words that can be found in the dictionary.......( sample password --- Zc6&#gH11pqH7) 12 characters is good 16and more is better.
Just remember that you should never run Lunux as Root, Root has administrative Privilages and you can severly damage your OS, you should always run Linux as the normal user.
WIndows has the market share of the OS's that are run on computers and those that write viruses write them for Windows .
Setup a firewall, if your OS does not have one by default, there are several good ones that you can install - if you are behind a router be sure to change the default admin. and login password also ( a router will/does also act as a firewall )
Read this for more on linux security: http://www.linuxtopia.org/LinuxSecurity/index.html
Possibly someone will come along that can give you more detailed information.
Edited by Ramchu, 29 September 2010 - 05:19 PM.