When we do a fresh checkout Unity does not remember that we are building an iOS app. In which file is that information saved and should I check that into version control?
You need to include the ProjectSettings folder in your version control system.
If you are using git, I recommend using this .gitignore file: Unity GitIgnore ยท GitHub
The setting for which platform you are building for is saved in EditorUserBuildSettings.asset in the Library folder. As with everything in the Library folder, you should not check it into version control.