".exe" executables are specific to Windows and--more importantly--to the x86 architecture. If you have the source code and it is in a suitable language, you should--with some work--be able to compile it to run on a Pi under Linux, otherwise, you'll need at least an x86 simulator and at worst a Windows system call translator. In any case, the program will run very, very slowly if you have to do it that way.
As for operating system...unless you have specific knowledge and reason to pick something else, use Raspbian. It has the best support for the Pi of any OS that will run on a Pi.
What I would suggest you do to start with is to set your Pi up running Raspbian and start working with it and particularly MySQL (MariaDB these days, actually). If you are planning to use some item of commercial software, people may be able to suggest Linux-based substitutes that are already available for the Pi. (I am presuming from the way the original question was phrased that you have been working with Windows systems.)