Currently my website (production server) already have a lot of code in it. And now I want to start using Git for my projects and setup a staging server for my team. Can anybody
Your suggestion looks ok, but I wouldn't let the developers push directly to the staging server. Instead, an integrator should carefully review branches and incorporate them into the main branch (or development branch if you use the git flow model as suggested by bUg.) * The same person would push to the staging server.
* Integrator: "A fairly central person acting as the integrator in a group project receives changes made by others, reviews and integrates them and publishes the result for others to use..."
1. do a git init in production server (is this safe?)
Yes it's safe, but you of course have to set very restrictive permissions on this repo.
I would probably start off by curl
ing the whole web site to a local disc, if I don't already have it.
2. clone the repo from production to staging server
You should probably have a "central" repo separate from both the production and the staging server. That one can be cloned and pushed as needed.
3. developers clone the repo from the staging to their local machine
4. push files to the staging server after finish changing
5. when staging is ready, push everything to the production
Replace "staging" with "central" and I think you're ok, but a bigger issue is how you'll work with branches and merging, as bUg points out.