IMHO, a high-spec graphics capability is not particularly important for video editing. We quite happily edit on a 4-year-old laptop with a modest graphics card.
However, this is one of the occasions where the installed RAM really does make a big difference. Digital video files can quickly become sizeable, especially if you're importing from a camcorder and editing/saving to (say) full DVD standards.
So although it's perfectly feasible to edit video on a machine with (say) 500MB RAM, that will almost certainly result in lots of hard disc thrashing and reduced performance, due to the routine need to use virtual RAM.
So assuming the machine will come with Vista, we do recommend you look for something with at least 1GB RAM, or upgrade to same. This will speed things up quite considerably on memory-hungry applications. Video editing is a good example of this. HTH.