Centrinos are generally a bit better (for laptops) than P4s etc. Better battery life and they aren't as slow as 1.6Ghz would suggest. They are better made for laptops in that they are more energy efficient (ie, cooler + quieter, better battery life), and have stuff like wireless technology built in.
Building your own is a complete no-no, it just doesn't happen with laptops.
Built-in wireless isn't that important. It's nice but you can always stick a Wireless PCMCIA card in and you're off. Make sure you get 802.11g not 802.11b though (faster).
Also it might be worth thinking about (shock horror) Apple laptops. They have pretty awsome battery life (mine lasts around 5 hours, as compared to some PC laptops which have about 90minutes of battery life). And the 12" iBook (aka the cheapest one) is pretty small. Not as small as the "ultra portable" PC laptops you see, but the iBook is fully featured (ie fast, DVD drive etc) which some of the small PC laptops aren't. Oh, and it's super quiet too. With the educational discount you can get them from about £600, or get a second hand one. Something to think about [/hard sell] B)