I am trying to figure out the best setup for GIT, with regards to having a local development server and a production server, or skipping the local development server. I visualize things below:

I am thinking of these two options after implementing GIT:


What is best? I feel we can skip steps by syncing right away with the production server, but it feels a bit dangerous not having a development server. But well, at the end every programmer basically has a dev server so that should replace this, or not…??
BTW: we create websites only; using PHP/MySQL, and only custom-made solutions.
Yes! You are right. You can skip steps by syncing right away with production server. Git is a version control system that help you to keep track your code.
Based on your question I noticed, your problem is that you are concerned with the code are being polluted in your production code. There is a branching system in GIT such that you can have separate two different branches or more, say, one is development branch and one is production branch on the GIT server. Once developer make some changes , they can push the code in development branch. Once, you have done enough testing on development branch, you can merge your code into your production branch and finally use the code in production branch and roll out to your specific client.
In addition, as there is only one git server storing your code. It is better to make a backup copy everyday. Then everything should be alright and can solve your problem.
Go back to your question, only 1 GIT server is enough
Hope it helps you.