Depending on budget you could probably go one of two ways, spend more and get a MacBook (never had one myself, but I expect the tool of choice by graphics artists and video producers (i suspect ad much Mac's style ad much as the software!)
Alternativley, spend less and by a windows laptop, it won't last you as long, but should be cheaper for comparable hardware.
Be aware that the latest spec will be disproportionately expensive, however end of line stuff may not be able to support newer software after as little as a year. (you could buy cheap and expect to replace it sooner) eg cheap Dell or or such from Tesco!
You should probably think about what software you'll want on it (sounds like you already have) as things such as video processing do benefit from certain hardware support.
It's worth buying a magazine that's does reviews etc as they'll review against thay kind of functionality, and you should get a better idea of other features you may or maynot know abouty. I'd advise againt the likes of Pc world, as in my experience they dont know their stuff so will not help you make a well informed decision - make your decision the choose where to buy.
No specific answers there, but the things I'd consider if I were looking again.
Worth looking at dell outlet, they somtimes do good offers (im not touting Dell, they just the only one I can remember at the mo!).