... how important is Damping factor in determining what amp to buy

If the speakers are not broken in, they are most likely to be over-damped.

My experience has been that is is important, especially for certain speakers. For example, just before the original 801, B&W made a speaker called the DM 16, which had very sloppy bass with a lot of quality equipment, but very tight bass with highly damped amps.
     Consider this. A speaker is an electric motor and can be used as a microphone. On tube and Class A amps, speakers on each end of the circuit can reverse roles as mic or speaker, as on a PA system in my dorm in college. I sent a signal through this speaker into every room in the building, about 300 speakers, from my room speaker.
     BTW, I used the speaker output of a Magnavox suitcase portable stereo's removable speaker, and simply added a female RCA jack to the PA speaker.
       Students were not amused to hear William tell Overtures at 5 AM of the first day of finals.. After my RA told the powers that be that I sometimes played this, I was invited to take a term off, but when I returned, my EE prof seemed impressed that I figured this out.
      My family also built our house, and with some supervision, I had helped wire it, complete with phone taps and speakers for music in every room, speakers that also fed my reel to reel, the tapes of which were quite startling in divorce court.  
       When a signal is sent to a speaker to play a note, the cone vibrates. When the signal stops, the cone is still moving back and forth. and is an electric motor. This movement sends the electrical signal back to the amp, and a highly damped amp will stop the cone sooner.
     Having said that, there does not seem to be a great difference on MOST speakers until the damping factor is below about around 150-500, at least on the Dm 16's. A 150 versus 1000 from the same company, does make a difference, ad these amp use the same pre-drivers and outputs, but more outputs.    

well well well,,,,,,,first of all,,, things have to be clarified here,,,,,1e taste is unique for every one ,,, so what can describe as tight bass for one could be muddy for another ,,, just like colors ,,,, smell ,,,,, etc etc
2e damping factor is highly degraded by speaker wire caliber and lenght ,,, for low inpedance amplifier ,,,,3e higher outpout impedance amp ( lower damping factor amps ) are less prone to that

now lets talk damping
my set up is the following
 i have 2 proel double 15 inches subs rated at 800 watts each 4 ohms
i drive theses with one k2 crown for each
my speaker wire is 15 feet long  10awg
the k2 damping is rated at 3000 at 8 ohmsso using a damping factor calculator  i made some test and came up with these numberswith the regular setup sated earlier  i had 127 df  because of the 4 ohms
i opened up the subs and made separate connection to each drive ( 8 ohms )  df when up to 150  approxdid not ear much difference , then i hook up the subs in series bringing the df to 453 approx
oh boy now i did get a noticeable difference in sound clarity and punch
witch drive me to change my next set up ,,
i will bring the k2 on the side of the subs  and use 6awg  of about 4 or 5 ft  passing trhue the port hole to connect the drivesaccording to the df calculator  this should bring me above 1400 df  of real damping
after this test ill be in a real position to tell if the sound difference is really different from 453 to above 1000if it is the case the next step will be  drilling the side of the subs , installing news wire terminals foe 2/0 awg wire  (00)awg
then with the shortest length of wire possible ( around 3 ft max in and out ) this shall bring me at around 2700 of damping  out of the 3000 rated by crown ..but i can already testify that just by changing the speaker impedance/ wire size and lenght , that sound did change a lot ,,,
so the real story about damping is this
unless your power amp is extremely close to the speaker , and the wire size is extremely large , you cannot benefit from the high damping factor rating from your amps
 the higher the damping rating is , the lower the amp output impedance is ,, and this is extremely sensible to the speaker wire impedance,

amps with lower damping are less prone to this therefore the tend to lose less of there df rating .
here is a good post about it
http://www.bcae1.com/dampfact.htm
remember ,,,, speaker wire should always be the largest you can physically  install or afford.
speaking of damping factor is futile if you run 18,16,14,12 awg  wire

When a signal is sent to a speaker to play a note, the cone vibrates. When the signal stops, the cone is still moving back and forth. and is an electric motor. This movement sends the electrical signal back to the amp, and a highly damped amp will stop the cone sooner.

Amp won't make much difference in damping, since there are already many ohms of the speaker's voice coil in series.  Overall effective damping factor is around df=1.5 at best.