OS = Operating System eg Windows 7/Ubuntu/OpenELEC
If you had just wanted XBMC then I would have suggested OpenELEC but as you want browsing as well, I'm gonna suggest Ubuntu !!
The reason I'm suggesting a Linux operating system rather than Windows is that its lighter on resources and therefore performs better on older hardware than Windows does.
My daughter (10) has
one of these. I picked it up for £50. Vista on it was extremely slow, so I ditched it for Win 7. It was OK but only OK. Now it runs Ubuntu 12.04LTS. She can browse with firefox and it runs XBMC in fullscreen with no issues. The only downside with Linux is that there can be compatibility issues with things like wireless cards and graphics drivers. So if you did go down this route then its work checking that the hardware is supported.
I realize if you know little about computers that this could sound a little daunting, but honestly it isn't and most hardware built within the last 5 or 6 years will probably be compatible straight 'out of the box'. Installing Linux is as easy as downloading a file and burning it to CD or making a bootable USB drive with it on.
Other laptops in our house running XBMC are an ASUS X71Q (which I picked up for £40 because the screen was damaged - replacement cost me £36 off ebay and I fitted it myself) and a Samsung R519.