About reflecting wordpress theme from github to production server

Github to production servers
What would you recommend?

in your current local development environment vagrant
virtualbox
centros
We are building a website in the form shown in .
There are two patterns of servers: Sakura Standard and AWS.
(EC2 is currently thinking of two instances, eventually auto scaling.)
Mainly updating the wordpress site, only the theme file
We are currently improving the workflow to manage git.

Recently, I finally started touching github
Could push from local to remote repository.
I read a lot of books, but it didn't show much

in a way that is reflected in the production environment from the remote repository I am writing to ask you what kind of environment you are working in.

As a workflow, push to github and confirm it.
After that, it will be open to the public, but
What tools do you use?

I'll write down what I've thought about in my own way.
·If you want to manually reflect it, install a remote repository on the production server and pull
on the production server. ·Use scripts and tools to automatically reflect
I would also appreciate it if you could include misrecognition and security risks.

Basically, I think there are a lot of A patterns in the attached file. Are there any people who use the B pattern?
I would appreciate it if you could tell me the advantages and disadvantages.