What is the best way to add my custom PHP functionality to a Drupal homepage?
The best way forward is to go ahead and create a new module. You can find the steps from this link .It also shows you how to create a block from code.

You can add your files in the module and then make a function call which returns the table and add it as your block content. You can then include your block in the home page from admin interface in any region that you want it to be.

Hope it helps.