1...The signal.
a. The disc or LP being played. (The ultimate limit on quality).
b. The playback equipment, disc player or turntable and pickup. (How well the disc's potential is realized).
2...The speakers.
a. Type of speaker (planar, box, etc) , and make and model.
b. Number of speakers and their placement.
c. The room in which the speakers operate.
3...Amplification.
a. Active circuitry.
b. Speaker wires (Importance depends on length required).
c. Interconnects (Importance depends on active circuitry details).
As a special case for LP's only, turntable mounting provisions may rank somewhere at the top of the list if you have a problem with vibration.