720 is good but at this point, optics, CCD size, compression, stability (use a tripod!!!), lighting and sound(!!!) also matter. A 720 or even 480 shot on a pro camera with good optics by a competent videographer will look better than a 1080 shot on a max-i-pad handheld with a teeny plastic lens.
If you use youtube, you upload a 720 and the viewer chooses a resolution suitable to their computer and connection. They can then choose 720, letting it buffer, if they want to see it over again.
When stuff moves in a video, it messes with the compression. Outside you'll have grass and trees blowing around; this guzzles bandwidth. Shaking the camera just makes stuff much worse and hard to view.
In short, the camera is a small piece of the picture.
PS, storyboard your stuff, don't just stand in front of the caemra and mumble through.