You can use parental controls to create white lists or blacklists, and they require a separate password than the password for the computer. If the generic accounts are domain users then setting a GPO for this setting would be the most effective.
In the event that certain computers are used by generic accounts only, you could use OpenDNS as your DNS servers and restrict as much as needed for those accounts. Just simply set up an account and point the DNS server entries to OpenDNS. When you log into the web interface you will have the option of blocking/allowing categories and specific domains.
I personally use Barracuda Web Filters for internet filtering and they work great, having tons of customization options. They’re not cheap though, but worth the investment. If you are looking to do this at little to no cost I would use a combination of parental controls and OpenDNS.