Retrieving specific images from Media Library

You are currently missing two parts: storage and interface.

And yes, it would make sense to handle this via media library, in which case you will probably be storing attachment IDs.

Storage is easy, Options API is trivial to use.

Interface is a little more involved. To this day WP doesn’t quite provide a native way to easily build interfaces. Facilities provided are a bit low level.

You can use Settings API, but it’s quite involved and doesn’t get you all the way to form elements or media management.

You might want to search for existing frameworks/helpers, meant to implement settings pages.