For the web stuff, you could force everyone to use your squid proxy.
You can configure squid to use apache's log format and use apache
tools such as webalizer to monitor traffic. There are also some tools
customized for squid.

There are a few ways you can go with a Web Proxy. If you want to force
it, you will have to allow outgoing web traffic only from your proxy
server. This is a given for any method.