And the biggest influence on sound quality is...

Approximately 50% of the sound that reaches your ears in a residential sized room is from room reflections. I've heard systems comprised of nothing but superb quality, well matched components sound horrible in bad rooms. And systems composed of mediocre components sound engagingly musical in good ones. All depending on the room and setup (positioning of speakers & listeners). Naturally some recordings are disasters that sound bad regardless of anything else, but in a good room can still deliver a taste of the artists.

If your goal is to hear performances where you get a real sense of the performers & instruments, deal with the room first. 

BTW, taming a bad room may not require expensive and non-homelike room treatments. In overly reflective rooms (more common than overly damped ones), there are many steps one can make to control those reflections. Rugs, shades & drapes, soft furnishings, textile art. David Wilson told me long ago that shelved books and records make some of the best acoustic treatments.

Bass response varies tremendously around a room due to the effects of standing waves. Sometimes simply moving one's listening position a couple of feet in one direction or another can turn anemic bass into rich tuneful bass (or go beyond into flatulance).

While electronic room correction systems like Dirac can make a big difference, one is almost always better off first minimizing the sonic elements that need correcting.