You're under no obligation to choose a license. However, without a license, the default copyright laws apply, meaning that you retain all rights to your source code and no one may reproduce, distribute, or create derivative works from your work. If you're creating an open source project, we strongly encourage you to include an open source license. The Open Source Guide provides additional guidance on choosing the correct license for your project.
Note: If you publish your source code in a public repository on GitHub, according to the Terms of Service, other GitHub users have the right to view and fork your repository within the GitHub site. If you have already created a public repository and no longer want users to have access to it, you can make your repository private. When you convert a public repository to a private repository, existing forks or local copies created by other users will still exist.
In short, the only thing you can safely assume is that you have no rights to do anything at all with this code. In the particular case of GitHub, you can fork the repository and view the code, but nothing more.
You mention supporting open source and We are considering to use your project for our site. However as github's licensing page declares:
From GitHub's licensing help page:
https://opensource.stackexchange.com/questions/1720/what-can-i-assume-if-a-publicly-published-project-has-no-license/1721#1721