Security is best done in layers, there is no end all be all single security solution. You should secure it first at the router level of your home network. Enable things like NAT and SPI firewall. Then on the client side you should just use best practices. ClamAV is a free open source virus scanner that works on most distros of Unix and Linux.
However, by design, Linux uses what is known as POSIX standards for permissions. Which allows r-w-x to owner-group-everyone. This is the basis for how permissions work in Linux. It has the concept of GUI > shell > kernel, meaning the kernel is only accessible through the shell which would require admin access and authentication to make any changes.
This basic design means there are pretty much zero in the wild self replicating viruses for Linux, Unix, or even OS X. As long as you use best practices you can probably get away with out using anti-virus software. Don't install weird unsupported packages. Make sure you use a strong password for your account (to avoid brute force attacks), and make sure you have services like ssh turned off if you aren't going to use them.
So, secure your router first, then your client machine next. You can also employ methods like openDNS and such to help maintain a black list of malicious botnet servers out there. You can also monitor your own network traffic through one of the many Linux networking tools out there. The router will not monitor what you do.
Learn how to read the system.log file as Linux will output everything you do to the logs, and it is great for troubleshooting and auditing.
