Using a public/free git server is not always good option if you want to develop something private that you don't want to share with whole world.
What I will do is:
- to install git on specific Linux server.
- to install Apache if needed on that server.
- to configure git server over HTTP with:
- one repository named by you with initial import if desired
- simple user management with one user with password
When the task is ready, you can pull/push your repository with your favourite git client.