There are a million different ideas and opinions circulating the internet and drummers heads about how to make drums sound good. Honestly, you can take any reasonably well constructed drum, and with good heads and tuning, you can make it sound pretty good. Because you are reading this, I will assume "pretty good" isn't good enough for you, and you are ready to dive head first into a bit of drum nerdery with me.

This outlines the path of vibrational energy through the drum:

At it's most basic, vibrational energy is created by striking a drumhead, transferred around the various parts of the drum. Some of that energy is lost (converted to a small amount of heat), and the rest comes out as sound. A couple of important notes:

More mass requires more energy to vibrate. Less mass = greater sensitivity
Materials that vibrate less efficiently (wrap/rubber gaskets, etc.) increase energy losses
The energy transfer from head to shell and back is controlled with bearing edge design- more contact = greater energy transfer.

This video demonstrates some of these effects: