For iOS redirects, you'll have to set yourself up for Universal Linking per the documentation here:
https://dev.branch.io/getting-started/universal-app-links/guide/ios/
This is very important for redirect behavior on iOS 9 and later. Please note that not all 3rd party apps and browsers support Universal Linking functionality yet, so you should test on iOS from iMessage or Notes initially.
As for Desktop, you can set your Desktop redirect on the Link settings page - this will not take users to the App store/Play store on Desktop, but to the page you set. You can use the Branch hosted text-me-the-app page if you want to have this as your default for Branch redirects, or your site homepage, or any other page of your choosing. You can add Deeplink data that will be used for all redirects by adding key/value pairs in the SDK or manually when creating a marketing link from the Branch Dashboard. You can also set a $deeplink_path value that will be honored for a specific link, and you can further set a $desktop_url that will override defaults if you want a different redirect for a specific link.
There are many options and ways for you to configure how your redirects work - all of this is up to how you set your Link Settings on the Dashboard, and if you choose to override these defaults for any particular link. For example, you might have default redirects to the App store set for iOS and a desktop URL set to your main webpage on Link Settings. In this case, a link created without modifying these values will take the user to the App store on iOS (or the App if installed), and to the desktop URL specified in Link settings if clicked from Desktop. If, however, you want to override and set $desktop_url as something else for a given link, say, to a specific page on your webpage using the $desktop_url key, on iOS the redirects will be the same but on desktop you will be taken to the set $desktop_url. For any of these scenarios you can specify Deeplink Data to be passed through.