For iOS, if you want to host on your website, you will need to write a webapp. It's not much more than writing an XML manifest file and providing a way of letting users know how to save it their home screen. (It's done from the browser UI.)
When the user elects to "save to home screen" the OS will read the manifest file, and download the referenced assets and store them permanently. It actually wraps the content with a small native application.
If you want to write a native app, you can package your site into an app using PhoneGap. You will need a Mac to build the app, or you can use Adobe's cloud-based build service. (fee involved)
You will need to join the iPhone Developer's Program ($99/year) and submit your app for approval, which is not a given, especially if it is simply a clone of an existing website.
Webapps and native apps are mutually exclusive. Webapps cannot be listed in the App Store. Apps cannot be hosted on your website.