Seven days is a bit quick for any beer, but any lower OG non-complex beer should be ready by 10 days. I'd suggest a mild, a cream ale, an English brown, an American pale ale, a hefeweizen, or American wheat. Of those, a mild would probably be quickest.
A highly flocculant British yeast would be the way to go for all except the hefeweizen, and pitching the proper amount of yeast means it would finish up quickly.
I don't recommend packaging a beer until at least three days have passed with the beer at FG, but then it can be kegged.