Whichever combination you are most comfortable using.
You can make almost anything do the job, the question is how much work will it take. If you are already comfortable with one methodology and the tools that support it, that will take less work than just about anything else.
Currently using mostly Filemaker and MySQL/PHP neither of which are a good solution for a multi-user runtime that is easy to install/manage. (FileMaker requires you buy the license for each computer - no networking on runtime)
Looking to learn something new and trying to determine what is the best/most popular option out there.
There are more answers to this question than I'm willing to list! Any answer that meets your requirements would do. Because you are familiar with MySQL and PHP, that sounds like a fine answer to me. Bundle them with Apache, and presto, you've got a web-server solution for a workgroup.
It can be multi-user, it is relatively easy to package, it can be free, and you already know at least the majority of what you need to get started. What more can you ask?
There are many other answers, ranging from MS-Access at the near-GUI end of the spectrum, running through VB/MS-SQL in the middle range, to C and a file based engine such as dBase or Jet at the "geek" end of the spectrum. Almost any answer could probably do, the question boils down to what works best for you.