- Always keep the OS with your wallet on it up-to-date with the latest security patches.
I think it's not always the best to immediately update your wallet software. Personally, what I do is that I read release notes and news. There have been cases when update had some bugs and was dangerous. For that reason, I always wait a little and if I don't hear complains, then I update the software. Of course that highly depends on release notes because sometimes you need to immediately update your software because of critical bugs in current version.
- Antivirus software should be used if your wallet is running on Windows.
I'm afraid antiviruses spy on you, especially free ones. Instead, I would use Virustotal to check whether websites I visit are safe or not and I would also check some files there too.