Tom Scarff is an expert in this field. He supported me on my previous midi project, "a midi controlled, pneumatically operated, fire breathing dinosaur named Lunarsaurus which I showed at Maker Faire.
So I turned to him for this project and found that he already had a kit (called a boarduino) ready to go.http://midikits.net23.net/midi_boarduino/midi_boarduino.htm
The Boarduino is interesting because of its size. It's tiny (.75" x 3.75") and will fit in a small spot and the price is good. I prefer to buy it assembled - one less variable.
The easiest way to get started is to put a 9v battery on the standard 2.1 mm. Here a word of warning. You need to keep the power source within spec. I left my battery plugged in over a week or so, it dropped down below 9v and the microprocessor (trying as hard as it might) lost its marbles. Fortunately one can re-upload the code and you are back in business.
You can also provide 5vDC to the serial pin or the board but be very careful as there is no diode to protect you for reverse polarity (as there is with the 9v external plug).