Down load the 30 day free trial to see how filemaker works. It comes with an Invoicing starter solution that may do much of what you describe here, but keep in mind this is just an example file. It can manage inventory, but not well, in my opinion. It still may be a useful starting point in seeing how you might set this up. keep in mind that FileMaker is primarily a development tool for creating your own custom database solution. If you acquire a working copy (get FileMaker advanced if at all possible to do so), you are setting yourself up to spend a significant amount of time learning how to work with relational databases in general and FileMaker Pro in particular.
You may also find this simple invoicing demo file useful as an easier to understand example of how this might work for you: http://fmforums.com/forum/showpost.php?post/309136/