OK, now that there's a lively discussion about this, I'll revise my answer.
Since the question was "what is the the most important part of the drum set," it's got to be the person whose butt is on the throne! Drummers run the gamut from people who whack and bash the drums at that never-changing fff dynamic to those who could make Tupperware sound better than a set of Exports. Without a body in that seat and something coming into contact with those drumheads, they ain't making any noise. At that point, it's just there to look shiny or dusty or whatever condition the set happens to be in at the time.
The drummer makes the kit. Examining a kit for type of wood / type of heads / bearing edges / etc will only give you a ballpark estimate; they'll sound better, worse. Maybe they just sound okay. Yeah, we can all agree that all that stuff will say something about the quality of the sound, but in the end, you will not know what they sound like until someone hits them!
I'm not the first person to say they think that the drummer's the most important thing about the set, but I agree with those who did say that 100%.