Server Sent Events are indeed an HTML5 convention, and should be widely supported. I’ve got it working in Mobile Safari, so it works on your iPhone. There are some things to be found on how to include the SSE into a native app, but it might even be more user friendly to create a mobile app. You’ve got some metatag-thingies which allow you to run your page full screen when it’s saved to the springboard. That way, it’s universally accessible by anyone with a browser, you don’t have to pay the Apple developers fee (if you haven’t done so, or aren’t jailbroken), and don’t have to go through their verification process to get it in the app store. Seems like a lot of unnecessary trouble to go through for a school project. Unless it’s about programming for iOS…
Don’t worry about the web being harder to develop for. I’ve managed to get something working reasonably with SSE, and have ZERO programming experience, so it’s definitely doable.