I would say that staging should be based on a git flow release branch. After a git flow release start and git flow release publish you can start QA work on that branch, including deploying it to a staging area. When the QA work in the staging area has proven the code ready for production deploy in production and do git flow release finish.
If you are using TeamCity, you can easily set up the server to detect new remote release branches and automatically set up builds for them, see here.