I would say that if you are going to pick one operating system to run anti-virus on it should be the Windows side.
Here are some basics of avoiding viruses:
1. Use a router.
2. Those e-mails that promise you things or request you to change you account info shouldn't be followed directly. If you think it is legit, go STRAIGHT to the companies web site. Any company with their head on straight will allow you to do the same thing via typing their web address in the address bar.
3. Don't visit pr0n or similar sites or do downloads from sites you don't trust, or much MP3 sharing for that matter, these are sure ways of getting viruses.
4. Don't use port forwarding to the outside world unless you need it.
5. Turn off services like SSH, RDC, ARD, etc. unless you really need them.
6. Run anti-virus and anti-spyware on your Windows machine.
I don't run anti-virus on my Mac, I do check it every month or so. Sure, it MIGHT mitigate the risk, but I figure if a virus goes in the wild, then I'll just disconnect the computer from the internet, take down my home wireless and then boot the disc from an updated anti-virus CD as soon as the fixes are available.