It would be best to start with Xcode. Create your project from the appropriate template with your best guess for a name and save it somewhere appropriate. When you save the project, you'll have the option of creating it in a git repository. Then, you can create a GitHub repository with the same name. I believe that once you do this, it gives you instructions on how to push a local repository. You can just run those command on the command-line from the directory containing your Xcode project folder. Then refresh your GitHub web browser and you should see all your files. Xcode will automatically detect and use GitHub as the upstream. I recommend against using the Desktop for Xcode projects. The Desktop could be under control of some kind of file sync service like iCloud. You don't want to mix that with git. It won't turn out well for you.
Topic:
Developer Tools & Services
SubTopic:
Xcode