Wheels

Bikes ride the way they do because of frame and wheels.

Upgrading wheels (and/or tires) will have, by far, the most dramatic effect on the ride quality of any bicycle. A more expensive derailleur probably won't shift better immediately (it might last longer) but will have no impact on ride quality. 

The gyroscopic effect of a bicycle wheel multiplies the perceived weight of its components at the perimeter. This is easily demonstrated by holding one of your wheels by the axle upright. Move it side to side as if steering your bike. Then spin the wheel and attempt the steering motion again.

While a certain amount of this phenomenon is desirable and is inevitable - aiding stability, the goal of improvement is reduction of this weight effect so that handling and inertial characteristics are improved. Minor weight reductions here dwarf weight improvements anywhere else. Inherent damping qualities among various materials still apply to rims and tires the same way they do to frames. And within the same material, load capacity being equivalent, less mass is a less-efficient transmitter of shock.