The easiest thing would be a [u]Sound Sensor Module[/u]. This particular one has an (amplified) audio output, an analog output that's proportional to the loudness, and a binary (on/off) output that's triggered when the sound is above a threshold. But, this particular board doesn't have a gain/sensitivity control and that could be a problem. (You can change resistor values, but I'd look for something else.)
By placing a sound sensor very-close to the drum head, you should be able to detect each particular drum.
You can also make or buy a [u]piezo drum triggers[/u] that picks-up the vibration directly. The commercial triggers are, of course, designed for MIDI.* I'm not sure if these things work with cymbals but it's probably worth visiting a musical instrument store to check-out what's available and to see how they work.
As a drummer in a band and an architect currently undergoing a Masters degree in interactivity,
Is this a school-project?
Have you taken any electronics or programming classes? If you need "technical help", I always recommend partnering-up with an electronics engineering student. This would be an easy project for a 3rd or 4th year EE student (and of course EE's also know how to program).
You need to focus on the "big picture" interactive stuff and you don't want to get bogged-down with easy stuff (or hard stuff) outside your field of study. i.e. In about an hour, I could probably wire-up a sound-sensor and write a little program to blink the pin-13 LED. (I've made a few sound-activated lighting effects and it's taken me a LOT longer than that, but it doesn't take me long to get something simple working.)
- Actually it would be "nice" to build this thing around the MIDI protocol, but that's another layer of hardware & programming and you might want to save that for later, especially if this is a school project/assignment with a deadline.