Everybody wants you to be safe, so much safety it hurts.
Using your head helps, it's a great first step. Yet, for one to use his/her head in a clever fashion, (s)he must be aware.
Before messing with Anti-Virus & Malware scanners, harden your browser, as this is the gate to nastyness.
Webtrackers and dataminers (those who make money from your online movements) slow down your surfing experience, and irrelevant advertisements might compromise your computer due to malicious software hidden in them.
Thanks to panopticlick, you can review how much data you are giving away.
here are some useful Add-ons, to help keep the computer healthy:
The Electronic Frontier Foundation is a non-profit who is concerned for your privacy. They offer really easy understandable guides to help you increase your online privacy. I have nothing to with 'm but I figured I should tell you about them.