How would I edit this video to how I want it?

I shot this video late 2012 on my iPhone 5 camera. But as I got my DSLR May 2013 and made videos using it, I can just notice the terrible quality of the footage shot on my iPhone, therefore I want to edit this video and give it a smoother and nicer look to it.

What I can notice about it now is the sluggishness of it, I can see the motion within the video therefore I somehow want to create more frames per second so that I can later show the action shot in slow motion without causing any, or too much blur.
Secondly, I just want the clip to look a little better in itself, HD colours, less light conflict with the camera etc.

I've access to Premiere Pro, and After Effects CS6.

Any help?

A (cough) paid (cough) plugin for after effects named Twixtor is exactly what you're looking for, but it's not perfect by any means, it is, however, the absolute best you'll get, making interframes is very difficult, twixtor just merges frames as best it can, it can look very weird sometimes but its key focus is on faking slow-motion on low fps footage.