By default Redmine is used to track the master branch of a repository. Using git symbolic-ref, you can set-up the HEAD to point by default to another branch. The command use to achieve this is:
git symbolic-ref HEAD refs/heads/mybranch
From now on Redmine will default track the "mybranch" branch when visiting the Repository tab. Read more documentation on the Git manual.
This document details the naming of the Drupal Git core, module, themes releases. It shows how to name your branches and release tags.