What is the most important muscle or set of muscles to work out?

The most important muscles are the chest, back and legs. Think about it, almost 3/4 of your weight results from just these three muscle groups. To train them, the best way is to use compund moves (which work more muscles at the same tame) like the squat for the legs, deadlifts or chins for the back and bench presses for the chest. When you will reach to a good enough poundage on these exercises, you can think of adding more muscle groups.

I would agree. Legs set the tone for the rest of your body. Simply working them out will release hormones to the rest of your body that will beef them it up. You could never do a curl in your life and get some decent biceps. But also equally important is your abs and core. This is not just for looks, although thats why we love them, but it also supports your whole body and keeps you strong and flexible.

The most important thing to work out in my opinion would be your legs because it effects the rest of your body most of time, like if you were jogging or something.