You have much (too much?) confidence in the security of the web sites that you visit...
If they have not been properly secured, an attacker can insert code to be run when you visit - a "drive-by" attack.
Even advertising can be poisoned in this way.
Cavey's suggestion of an integrated suite of security software is the sensible solution.
One does need a memory-resident guard against infection equipped with a link-scanner to identify known malicious/
compromised web sites.
Yes, one can avoid a great many problems by selecting where one surfs with care but that does not provide 100% protection.
A properly-configured firewall is also a necessity.
I would not let a kid near any PC on which I performed any financial transaction or on which I kept sensitive data of any sort.
Net Nanny programs do work - in fact, they can be a very blunt and restrictive tool. When my son was at school, researching for
an essay on a World War 2 topic, that installed on his machine stopped him visiting the Imperial War Museum's site due to the
references on it to German national socialism. The program also sent me reports by email of which web sites were being accessed.
You may think that is a bit like "Big Brother" but I called it "Big Daddy" and the knowledge that I had this capability was a deterrent to
any exploration "off piste", shall we say! I still regard such programs as essentials for responsible parents unless all activity on the
machine takes place in a common room like ones living room where it can be overseen in person by the parent.