Recommend me a digital recording setup

I have a set of electronic drums, and I also have a laptop. I want them to work together.
I'm specifically I'm looking for software and hardware recommendations so I can record what I'm banging out on my drums on my laptop. I'm interested in recording more than just the sound though. I would like to have the actual outputs for the separate triggers, so I can edit it and change the sounds after the fact. So MIDI, I'm guessing? I really am fairly ignorant at this point, so any advice would be great.