I'm not sure how things work in the US, but here in the UK you can either get a broadband modem (Connects via ONE Ethernet port, or USB) or broadband Router.
The router is like the Belkin that you have, allowed connection over a network, as well as to the internet - and more often than not - to other machines.
AirPort express is simply a box that incorporates Wi-Fi, USB and AirTunes. Your own router/broadband modem plugs into the AirPort express, 'adapting' your router to become wireless. It also allows you to stream music, and wireless printing.
The AirPort Extreme base station allows connections to more computers at a time, and at a wider range - I believe. However, you still connect your own source (broadband router, or broadband modem - the base simply 'beams' the signal out)
However, you can order AirPort Extreme with a built in modem - allowing you a wireless internet connection, as well as network, all from the base - without connecting additional modems/routers, as it has one already built in.
I'm 95% sure thats correct. But AirPort Express does not have a router/modem built in - 100%