The Vimeo code is iPad/iPhone friendly but probably your file size isn't.
You can't just put a video on a website and hope that it will play on all devices. You need to either provide different versions of the movie for the various devices or cater to the lowest common denominator and supply a small compressed file for iPhone users.
Remember that mobile devices are more often than not struggling to download movies over shakey wireless networks.
Apart from a reasonable file size, the main thing to do with video aimed a portable devices is to have them load a poster image and prevent them from auto loading. I use an HTML5 player with flash fallback. Autoload is set to none in the code so that only the poster image loads along with the page.
I use the VideoJS player which uses HTML5 with fallback to flash. The HTML5 part of the code would be like this...
<video controls="controls" preload="none" width="640" height="480"
<source src="http://website.com/folder-name/movie-name.mp4" type='video/mp4' />