Great to hear you got started somewhere. I think custom is probably the route you want to use. We have the { JFBCLogin} tag now, so you can use that to insert the "Login With Facebook" button, and then individually add any other text or links you want to as needed. Our Login module isn't super flexible right now, and that's something we want to improve in an upcoming release. However, with such specific needs, we probably won't have every option you need.
If you are changing code though, you can likely use our JFBCLogin module as a starting point and just remove the features you don't need. You can do this easily using a template override, which will prevent your changes from being overwritten if you upgrade. For information on how to create a template override, see the bottom section of the below article:
www.sourcecoast.com/extensions/troublesh...ng-joomla-extensions
Good luck, and let us know if you have any specific questions on how to implement something!