How important is S/N Ratio....?

Specs are near-meaningless. At best, advisory.
Don't worry about them. Would you junk out an amp you liked with a 90db snr and replace it with an amp you Didn't like with a 110db snr? Didn't think so.

from wavetrader:
If you have equivalently low levels of noise but when music is playing you have within it some correlated noise that follows with the music (harmonically or IMD related) then this gear will sound much worse (even if they both share the same "on paper" S/N ratio)"

Just what does above quote mean in standard English?

135db and I can hear it!!!!!
Human hearing dynamic range is somewhat lower than that...
A sound at 135db would burst your ear drums or render you incapable of appreciating hi-fi.
Therefore, a sound '135db' down is either....So far below hearing limits as to be nearly, if not completely unmeasureable OR referenced to a sound so loud that it would Hospitalize you.
I am not even going to go to the 'Weakest Link' end of town where who cares if your caps are 135db, when your output devices and the REST of the circuitry are no better than 100db?
I repeat:: Specs are nearly meaningless. If you purchase something based on specs rather than quality, you may be surprised. It could go either way!

http://www.cs.cf.ac.uk/Dave/Multimedia/node271.html

This article claims 96db range....from dead quiet to loudest.
other articles claim up to 120db. 'Pain Threshold' is usually quoted at about 135db. I don't know what OSHA says, but I'll go out on a limb here and say that an accurately reproduced Jet takeoff at 120db will, if repeated monthly, take the edge off your HF hearing within a year or less.
At that PEAK level, the sound of a car door slamming or a gunshot would be enough to hear next door.
At this point, 'ya gotta wonder if your speakers are up to it! A 120db slam is pretty ambitious and even if your speakers CAN do that (What kinds CAN do that?) I rather suspect you would need your own substation to power the multiple kilowatts of amp necessary to keep up.
I haven't done the math, but you'd need speaker of fairly high sensitivity and power handling capacity with huge dynamic limits.
I tend to agree with those saying damping factor is not that important after a certain minimal value, but that bein said, nobody has mentioned the other half of the equation, that being speaker 'Q'. A critically damped speaker (Q=.707) coupled with a reasonable damping factor may actually produce thin bass.....Is this the opposite of what the fans of 'bloom' hint at? I'm not clear on that point.

Anyway, good luck, all you fans of accurate jet take offs and I'll be sure to buy stock in a hearing aid company. soon.

Keep in mind I didn't start the Jet takeoff thing.
I lived near El Toro MCAS and heard F-4 takeoffs which even with them being as easy as possible...no afterburners or aggressive climbouts, you could hear them for several minutes echoing thru the canyons. I was at an airshow and witnessed a flyby of a Concord! Man, that thing was LOUD.

This whole thing needs to be thought thru more thoroughly.
How quiet is your room? 40db at 0-dark-30? Let's say you can play it pretty much as loud as you'd like...not likely but we can dream! Subtract 40 from 120 and you've got 80db range. This is more than Vinyl is capable of and stretches the practical (NOTE: practical, not measureable) CD limits.

Sorry, this is a non-starter and a fine example of wishful thinking and specsmanship taking over!

There are great numbers of Credible Systems which use hi sensitivity speakers coupled to low power amps. These systems en toto draw less than my bedside reading lamp.