Please excuse my naiveté: exactly what types of websites am I supposed to steer clear of to avoid contracting malware infections?
The obvious answer is: Any site dealing with Porn/Warez/Cracks.
In my experience, though, nothing is truly "safe." There are just varying degrees of safety.
Malware targets youngsters via sites set up for them because they don't know any better when asked to download something.
I can remember when wrestling sites were a prime source of infection.
I was browsing Philly.com a few weeks ago and clicked a seemingly legit link and was hit with a pop up for a rogue anti-malware app that produced a flash video of said app pretending to "scan" my computer for baddies.
A lot of people are infected that way when they download and install these rogues...
Heck - I've seen legitimate security websites hacked (html code injection, etc...) and people getting infected that way.
Use a good anti-malware remover. Malwarebytes' Anti-Malware is one of the best today. Update and scan at least weekly and remove all found. Very often the first tool recommended when a known infection has gone on attack.
Make sure your browser has the correct security settings including 1st party cookies ONLY, block 3rd party cookies. Use a safer browser, Firefox is one which is certainly more secure than IE.
Add the WEB of TRUST add-on to the browser. Won't stop you from going to websites but will give you a warning that a web site may not be trusted.
Use a program like SpywareBlaster to add to your protection.
Keep your programs up to date. A safer computer is certainly an up to date computer.