Almost every module needs settings, so it's a good idea to get this under your belt first.  The core modules provides many examples of how to work with module settings.  To be clear, you have module settings for each instance of your module and tabmodule settings for a module in a particular tab.  In this case you would use module settings.

Module setting name is of your choosing when you write the code.  The core framework provides all the plumbing to retrieve and to save the settings into the DNN database.  I recommend prefixing your module setting names consistently that way it will be easy to indentify them when querying the database later.

As a bonus, look into implementing Iportable interface.  With this you can easily export your module settings from one DNN installation to another.