How much do I need to spend to get a preamp that sounds better than no preamp?

No preamp is still a preamp. It’s just built into the device.  

Generally a good stand alone preamp fed by the line level output of your source will be better than an amp fed directly by the volume controlled output of your source.

FWIW, devices that only include line level outputs are less complicated, have better interior layouts, and sound better than “do it all” devices that include direct volume control capability.  

It’s really pretty much about the two methods of volume control.  My ET7 and my SP20 pretty much whoop the volume controls that are available to me using any of my $2k level sources.  I’m better off feeding undegraded line level into either SP20 or ET7.  Same was true with ET3SE or PV8 or PV11.  

Generally a good stand alone preamp fed by the line level output of your source will be better than an amp fed directly by the volume controlled output of your source.

Sorry but you have this wrong, volume controls in sources (cdp’s and dac’s) don’t feed the amp, they have output buffers after their volume control stage, and in many cases this buffer is the same or even better at driving an amp with lower output impedance and better current than some preamps outputs can especially tube preamps.

Cheers George

I am using simple terms to keep from obfuscating the issue in play.  

I’m happy to agree to disagree.  

But experience tells me that, as seems to be true of most forum dwellers, I should wait with bated breath for you to have the last word.  

Go go for it. 

Sorry broadwayjoe you are not even using simple terms, you simply have it wrong, accept it, if your going to state things, check to see if you have them right.
The volume control from sources such as cdp ,dac, even computers ect do not drive the amp/s, their output buffers do (BIG DIFFERENCE to what you implied), which as I pointed out are more than up to the task, in most cases.

Cheers George

To George and all. I have been listening to my Luminous Audio Axiom II with Walker mod, single ended 3 in 2 out, with remote, for a week now, and I have to say, I am connecting with the musicians, as well as the mixing and mastering engineers who have worked on the recordings, like never before. A veil has been lifted, the colorations are gone, and nothing is missing from using my 2 expensive preamps ( will not mention what they are ). I am feeling lucky ( punk ), that the synergy is working for me, and quite happy I made the move. The background is dead quiet, as there is absolutely no noise, hiss, hum ( etc. ) in my system. Thank you George for steering me in this direction, as I always thought an active preamp ( with gain ) was absolutely necessary( and I have been at this for 50 or so years ). Of course, experimenting with my pro amplifiers, with their built in volume attenuators, allowed me to hear this as well, but now I can use my favorite little amplifier, which I could not, successfully, use before. Cheers ! Enjoy ! MrD.