Any computer will be fine, but the better the processor, the faster the clip is gonna get rendered. Also, SSD because you are constantly reading/writing from the local drive while editing the brute material
Nevertheless, more important then the hardware is the software you gonna use. People who edit videos use Apple's computers, because of their software. You gonna go crazy editing on Windows bundled software. You gonna have to buy Cyberlink PowerDirector, but thats the worst offering and still gonna give you headeches.
I sugest you get hte current macbook air, they have recently upgraded to haswell and PCi-x flash drive as the local drive. That is 2x faster then any Sata III SSD, its speed is equivalent to the OCZ revodrive. So for the time, its a computer wich have a low "apple tax". More importantly, their bundled software, iMovie, is a semi-professional editor
I expect a lot of people on this forum to say Apple is garbage, but reemmber that they are gamers, not creative professionals. I also sugest you contatc the people who make youtube videos, send them a message on youtube, and they will tell you the computer they use.