Opera at home and firefox at work. Couldn't live without mouse gestures now. Prefer the look and feel of opera (except the ads).
Oh and Lennon if you're going to be smartass, so am I
The web is not a "small" part of the internet, the web is a service provided by the internet. An internet is just a wide area network of networks and the www is the "web" of interconnected HTML etc. pages that reside on servers that form the internet. You're right in that the internet provides many other services aside from the web though (FTP, email, distributed computing, to name a few).