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

Al, I agree, but when people refer to DF (including this discussion), they mention control of the woofer.  The effects of complex load should diminish when source impedance is 10 times smaller than the load.  DF=20 should be a good choice.   At this point I would prefer output impedance that is constant with frequency over high DF.  My amp's output impedance varies from 0.002ohm@5Hz to about 1ohm@20kHz.  Tweeter's impedance is very high at 20kHz but there usually is some network of resistor in series with capacitor, parallel to the tweeter.  Can this affect the sound?

One more thing about control of the speaker at low frequencies - amplifier might be the one that is uncontrolled.  Audio amps are designed often with assumption that they will play 20-20kHz.  Because of that, they are often equipped with servo on DC that has bandwidth of few Hz.  Presence of very low frequencies coming form the source (movie, TT vibration, special effect etc) can make this servo to overcompensate and go crazy (unstable) affecting audible band.

Al, I agree, but when people refer to DF (including this discussion), they mention control of the woofer. The effects of complex load should diminish when source impedance is 10 times smaller than the load. DF=20 should be a good choice. At this point I would prefer output impedance that is constant with frequency over high DF. My amp’s output impedance varies from 0.002ohm@5Hz to about 1ohm@20kHz. Tweeter’s impedance is very high at 20kHz but there usually is some network of resistor in series with capacitor, parallel to the tweeter. Can this affect the sound?

sure! of course! The RLC network is frequency dependent. isn’t that the reason for Zobel networks? The Zobel is for the power amplifier (not the speaker) even tho’ some manuf recommend attaching the Zobel to the speaker’s terminals rather than the amp’s output terminals.

OH MAN AGAIN...

Interesting to hear you Gurus going back and forth...

Need to reread this several times , list those for and against an effect, throw out the high and the low - and then consult the Russian Judge!

And in a some-what related question: I am presently using a Phillips High Fidelity Labratories Pre-Amplifier(1980?) - would the damping factor be affected if I switched to a Line-Level triode preamp (like the Wolze I have)? Does/can the preamp affect the damping factor of a amplifier?

heh! heh! heh! ;-0
And, here you thought you asked an innocent question! ;-) 
Also search the archives for damping factor discussions. There is MUCH written on this topic....
And here's some more dope on the subject for you to read (seems to fall in-line with what Ralph/Atma-sphere was saying that DF of about 20 is sufficient):

http://www.butleraudio.com/damping1.php

Here's a further link:
http://www.dissident-audio.com/Loudspeakers/CriticalLSDamping.pdf

Correction to my previous post:  When I said "solid stage preamp" I meant "solid state power amp."  Not sure how that error occurred.

Regards,
-- Al