OK so lets look at this another way
you are thinking of installing a NAS. many NAS devices these days run more than just network storage
you mention you are thinking of runnign an instance of a MySQL server on the NAS, so that suggests to me that the device you are buying, whicvh you don't identify has more capability than 'just' being a NAS. its running a MySQL server, so it can probably run other services.
you mention you want to run some applciation on two PC's connected to the NAS, you mention you want a GUI application. so as I read it your options are
either run the MySQL server on the NAS, write an application in either Access, Delphi or a traditional language such as .NET or Java
or
assuming your NAS supports running a webserver consider a web scripting language like PHP, ASP/ASP.NET, PERL Python and so on.
if your NAS can run other services then you coudl run somethign like Squeezebox server to provide music on demand to your home. the question I suppose is, is how capable is your proposed NAS box, is it a dedicated network storage box providing storage for any attached PC or is it a server box which can provide numerous services to a small network
the difference between the two is that the web scripting requires there to be a webserver somewhere, and many NAS's use a webserver as a mechanism of managing the NAS. so your NAS may already come with the webserver capable of supporting a web scripting language such as PHP. that means your GUI is web forms in a browser.
you asked for free ydpont get much cheaper than MySQL server and Apache, runnign a acripting language like PHP.
Python is free, so Is Java. .NET isn't, ASP may or may not run on a webserver.
ultimately its your call, after all you know what NAS you are thinking of buying, presumably you know what that NAS can support. without knowing in detail what it can or can't do all that can be be done is to suggest alternatives. if its confused you then I'm sorry, but mebbe thats apart of the problem in that you have already confused yourself by not identifying what you want beyond vague generalisations