A common misconception is that a medic's primary objective is to keep everyone else alive. But it's far more important for a medic to preserve himself, than to save any other class. In this respect, on the high priority list of every OTHER class, keeping the medic alive should be near the top.
Unfortunately, this priority is neglected much more often than a medic neglecting to heal someone.
Sombrero -
Demoman is a pretty easy class to learn. But RED is a very skilled demoman. You should spectate him now and then. You'll probably learn a lot.