optimizing file size or performance

Can you be more specific about how these videos will be hosted and what concerns you have about performance? Hosting videos directly on your site is generally not a great idea because the one version that's there is the version that everybody downloads—this doesn't work well for desktop vs mobile users, or even mobile users with varying data plans. A streaming server like YouTube will actually make well over a dozen versions of your video and serve different versions to depending on their bandwidth or network connection. A video in a native app shouldn't have an issue playing back as it would be local in the app, but if you have a specific use case and concerns in mind, let us know and we can be more detailed.