How can we really be "invisible" on the internet by only cleaning out cookies and use proxies?
We can't, because every damn browser has a UID, further on, in particular, anyone inside USA, or browsing a website whose server is located in USA will be tapped by NSA and the data is stored indefinitely.
Just look at this site alone. When we visit Wisegeek, we are also in contact with other sites.
Chrome is one of the worst browsers when seen from a privacy point of view, but Firefox since Google got involved isn't much better. There are tons of "phone home" stuff inside the browser, such as "safebrowsing", yeah. You really need it?
The fear mongering among the Mozilla people is absolutely ridiculous. As soon as you visit their support page, they jump on the monkey button as soon as you do and tell you that you don't have the latest browser (with the latest security holes and other new "wonder features" pinging home).
If you know a little bit, then even an old and "outdated" browser is safe to use, period!