In my project I have settings.gradle, gradle.properties and gradle-wrapper.properties files. Which of them should be checked in a Git repository?
All of those files should be commited as they all contain information critical to the build environment for the project.
The one exception would be if you needed to create a local.properties file to override or supplement those files on your computer specifically. The Configure your build section of Android Developer site has more information.
Additionally, when in doubt a good rule of thumb is to use a tool like gitignore.io to generate a Git gitignore file. It generally contains sane default rules on which files should be excluded from source control (and thus included).