how fast is this new centrino processor compared to the other 2 big cpu's? what exactly are the advantages of having a centrino cpu also?

Centrino isn't a cpu - it's a platform for notebook computers comprised of the Pentium M processor formerly known as Banias, Intel's 855 chipset family and its Pro/wireless 2100 mini-PCI Wi-Fi card.

In other words, Centrino is just the name for somewhat new technology bundled together in one marketing ploy.

Look here (http://www.theregister.co.uk/content/3/29721.html).

how's this computer look then?
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=3419065160&category=31546

I don't know much about picking one laptop over another. Maybe someone else could help you here.