Automate configuration after new/hosted installation

This sounds like a perfect use case for WP CLI, all you need is SSH access, which many major hosts now provide. Many of the features you are asking for are already provided out of the box. For others you should be able to create your custom WP CLI commands.

Some examples from the doc:

# Install the latest version from wordpress.org and activate
$ wp plugin install bbpress --activate

# Install the latest version of a theme from wordpress.org and activate
$ wp theme install twentysixteen --activate

# Create post with content from given file
$ wp post create ./post-content.txt --post_category=201,345 --post_title="Post from file"

Ivelina Dimova just gave a great lightning talk about the WP CLI at WordCamp Europe, even though I am not finding the presentation online right now.

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