What is a good process for full development cycle - from git to production server?

We have around ±130 projects:

• ±50 Custom Old Cms Projects
• ±40 Wordpress Projects
• ±40 Laravel Projects

The first one quite often requires unique environment setup (specific php, mysql etc version) the later two are quite consistent but might have some projects that require additional modules/configuration aka I don't see a problem with having one setup for all of them.

I'm trying to restructure the whole deployment process (currently it's all manual + a lot of problems arise from having completely different environments on each developers machine and servers) from Git/SVN to servers to be automatic. Problem is that there are so many options out there (some of which I don't have a complete understanding about them) and because of the current setup where I have to do everything manually + other responsibilities - I barely have time to lea all of it.

That said I'm looking to find out a good process to handle this issue with additional services/products like GitLab CI, Docker, Vagrant, Heroku etc.

Is there a well known process for this or what is yours if you're were at a similar situation?