Actually you want to filter out some of the folders inside "MyAwesomeGame", especially the `Library` folder, but also "Logs", "obj", and "Temp" (if there is one).
If you go with Git (highly recommended!), there are other hosting sites as well even if Github is most known. (GDTV uses Gitlab for example, and there is bitbucket.org, too)
Make sure you add a `.gitignore` file to your project, and add it *first*. A well-tuned ignore file will have the Library and other things listed so they won't get added into your git repository.