>IMO, the first step should be a good CI build system TFS or TeamCity can both pull from Git to do the build. TeamCity can also do the deploy, but you have to setup all the steps manually. If TFS is used, then ReleaseManagement is the Microsoft deployment tool. Another deployment option is OctopusDeploy.
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>Doing the build locally from Visual Studio is problematic and can cause issues. Generated binaries and NuGet-able binaries should not be stored in version control. Git is especially bad at binary files.

I discussed that with our Git specialist and we agree that OctopusDeploy seems to be what we would be needed. It might be a little too much for our present needs but on the long run, we would definitely need that. We would probably starts by doing some of those deployments as is but will eventually use power tool to automate all that across various environments with the benefit to update other things such as IIS, Main.ini file, etc.

Thanks for the reference