I read somewhere that whenever someone upload a project to Github, they should always include a readme file, for legal reasons.
That would be a license, not a readme. GitHub actually provides you a selection of licenses you can choose when you create your repository.
Since you said your project is 100% free and open-source, you can either consider GPL licenses, the Apache License, or the Creative Commons license.
GPL licenses require you to put the licenses everywhere if you continue with the project.
Apache License is what most of us GitHub project creators use.
Creative Commons is like what the Wikipedia does, sharing information without saying who the author(s) is.