如何使用Git管理项目变化以及开发流程？

I have a rails website that is about to be sold to different clients with small variations for each client. In the mean while I'll be definitely developing fix and/or modifying the "common" parts of the project. So how would be the preferred way to manage this developing process with Git? Initially I though that "Branching" would be the way to go... but 1 min later I realized that anything committed on a single branch wouldn't available on other branches and this way to fix something in the "common code" would result in multiple commit to each branch. In the end I though that "Tags" might solve the problem since it's a way to track variations on a single branch. I couldn't think of any other options. Maybe someone can help.I have a rails website that is about to be sold