Fedora 18 security questions.

[William Mattison]

I have a single desktop connected only to the internet.  It's dual-boot: Fedora 18 and windows 7 home.  In Fedora, it has more than one user id.

I skimmed/read through the Fedora 18 security guide, and much of the Fedora 18 installation guide and the Fedora 18 sys. admin. guide.  As best as I can tell, the only thing that I need to do is make sure the default firewall is active as per this section of the security guide:
http://docs.fedoraproject.org/en-US/Fedora/18/html/Security_Guide/sect-Security_Guide-Firewalls-Basic_Firewall_Configuration.html
and make sure the system stays up-to-date ("yum" seems to be doing that).  But my experience, understanding of computer security and sys. admin. are extremely poor and beginners level.  I'm assuming that what these guides say about multi-computer systems, LANs, WANs, servers, etc. does not apply to my system.  Any thoughts or suggestions?

Windows has security essentials and malwarebytes scanning browser traffic to detect and block malware, and scanning the hard drive to find and remove malware.  What does Linux have corresponding to that?  I'm just about certain that my old Linux system is infected with working spyware.  I'd like to have something like security essentials, malwarebytes, etc. on my new Linux system.

Thank-you in advance for your help.
Bill.