If you're hosting the website videos on your web hosting account with your web host then I personally would use the WebM format which seems to be supported by all browsers.
Another alternative would be to just host the video through Youtube and then embed the video into your website and allow Youtube to do the hosting of the video which would save you bandwidth and server space.
But for hosting the video yourself I would use the WebM video format or MP4 format so it will work with most browsers.