The MIDI sound module just has the 5 pin DIN connector input, so I would just need to be able to connect whatever arduino board to the module with that.
Any Arduino will cope with this. You need a small circuit that converts the signal from the serial port to a MIDI socket. You can buy these or make them yourself, here is one I made earlier. http://www.thebox.myzen.co.uk/Hardware/MIDI_Shield.html
Or you can buy one, just search for "MIDI Shield" Here is one MIDI Shield
Then the software is quite simple, this project has the basics of what you want although the switches are some what different. http://www.thebox.myzen.co.uk/Hardware/Pendulum.html
What you want to make is not called a MIDI controller, that is used to described a box that sends MIDI control messages not note on messages. You want a MIDI keyboard.
However exactly what you want with software and a full explanation of how it works, along with lots of other stuff can be found in my book. Arduino Music projects