Aperture, in my opinion, is more of a workflow tool not meant to be used as a primary source of editing photos. I also believe it is better than the alternative (Lightroom) because of the way it archives originals. While it has some very useful, albeit basic, editing tools, it is no match for Photoshop or even Photoshop Elements.
I like to load all photos into Aperture, sort, delete, etc, and then any real adjustments I need outside the basics available in Aperture, I use photoshop.
Aperture however is a memory hog. I am sure it will run on the MacBook Air, but I am unsure it will run in the manner you or any other sane user would hope for. I believe that Lightroom, a tool similar to Aperture simply made by Adobe, may run smoother but I cannot tell you for sure. I can recommend you download a trial of both and pick your poison.
Some may say they use Aperture only, this is acceptable to some but not to me.