I've owned a dell inspiron 640m for the last 2 years and have found it to be a good laptop - enough built in cpu and onboard graphics to do anything (including my various university maths/science related projects) other than play 3d games, long battery life (i can still get 3+ hours out of my extended battery), a high res screen (1440x900 on a 14.1 in laptop; better than 100dpi

), and the warranty service is quite good (dell sent a guy out to where i work 2 days after i reported the problem, and had the part replaced).
Dell comps (at their normal prices) are a bit more expensive, but you get that back in service.
One thing i would recommend is to wait around, keeping an eye on the website of whichever vender you decide to go through, waiting for a good deal, as you can save 20% if you purchase at the right time (especially with dell, they often have various deals running).
In terms of components, on-board graphics are probably good enough. ram is cheap, and a good way to future proof the laptop, although if you get 32bit win XP, it can't use more than 3Gb. Probably the 64bit version of the OS, with 4G of ram is best.
There are 2 lines of laptop cpu's around - centrino, which is the laptop version of the core2, and the atom, which is a specifically made low power cpu for mobile devices. The atom has less computational power (not enough to run vista), but longer battery life, and the new EEEpc, Dells new mini-laptops and a few others use this. Any centrino based cpu is good enough for almost anything you would want, and the Atoms are good enough for all the common tasks you list (running word, web browsers, playing videos,...)
RE: the guy about linux above-- some vendors do support specific flavours of linux (eg dell; ubuntu), and yes while office 2007 support isn't available under linux Office 2003 itself can be run in Linux (google wine, crossover office, or just office linux), and OpenOffice is probably more compatible with office 2003 than office 2007 is.
If you do get a laptop with a graphics card in it battery life will be reduced, but then all the shiny goodness of vista will run well.
integrated wireless -- any new laptop of any type will have that.
RE:Spec8472's comments - good post (i read it after i started writing this and we seem to think along the same lines), although i'm not sure about the power comments - i run win xp, and i've a sleep mode which returns to fully operational in about 5 seconds, and uses about 1% of battery an hour, and it'll drop from sleep to hibernate (0% battery per hour) after a specified amount of sleep time (so i normally have it set to sleep on close the lid, or 5 mins, then hibernate after 2 hours - that way if i walk away form my laptop on friday, i know its only lost 2 or 3% battery life on monday).
edit, what was here before wasn't quite right:
One last thing to note: some Vista licences are also licences for XP -- so if you have a choice you can get vista, then borrow someone's xp cd and use your own serial no. to install it. (borrowing both their cd and their serial number is a no-no though, the activation process may result in both computers having issues if the same no. is used in multiple places.)
"Can I downgrade my OEM version of Windows Vista Business to Windows XP Professional?
Yes. OEM downgrade rights for desktop PC operating systems apply to Windows Vista Business and Windows Vista Ultimate as stated in the License Terms. Please note, OEM downgrade versions of Windows Vista Business and Windows Vista Ultimate are limited to Windows XP Professional ..(list of cd versions which work)..There are no downgrade rights granted for Windows Vista Home Basic or Windows Vista Home Premium."
(wow, what a long post, now if only i could be this productive concerning the paper i'm supposed to be working on ...)