For most home PC users, fairly secure is perfectly adequate, and that's what we'll be concentrating on below. In a week or two I'll get into details for power users, but for now I'm going to concentrate on a particular presumed reader: a home user who's fairly new to the Linux desktop, who's using a packaged distro, and who's not intimately familiar with PC security -- a 'recovering Windows user', let's say.
Fortunately, Linux is a wise investment; you already have, or can easily find for free, virtually everything you need to make it secure. There's no need to buy hundreds of dollars' worth of security utilities and services, though you do need to learn how to use what you've got. But before we get to the Internet security matters promised in the headline, we have some housecleaning to do.