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

I have an easy way to evaluate a pre-amplifier.  A few years ago I obtained a Stax tube electrostatic headphone system.  By chanch I also had my then Audio Research LS26 tube pre-amplifier sitting right next to me.  Anyway I simply hooked my Stax system thru the LS26's record out outputs.  As at the time a long time user of Stax headphone systems, I immediatly noticed how the audio reproduction was greatly improved.  Not just a little bit but a definite audio improvements.  Now when I would take an audio source and hooked it up directly to my Stax system, the audio quality went way, way down.  Presently I am doing the same with an Audio Research LS27 and both a solid state as well as a tube Stax system.  As the LS27 has both a ballanced as well as a single ended output, with a pair of adapters I am able to hook up two different Stax systems.  Now in between I tried tje same thing with a Classe DR5 solid state pre-amplifier and got different results.  Now the Classe was a very good pre-amp, but the Stax systems would sound better if connected directly their audio source as compared to thru the Classe pre-amplifier.  Which brings me to the opinion that the question of whether to use a pre-amplifier or not might just rest upon the quality of the pre-amplifier itself.  The results are so much easier to compare if done thru a high quality headphone systems as opposed to a regular speaker based audio system.  Unlike a speaker bsed system, the results are easily noticible, and immediatly thru a quality headphone system.  Thru my LS27 I can match output levels and with a push of a button on my remote control go back and forth easily.  And again, the results are so easily apparent immediatly.  No need to go back and forth countless time to evaluate different audio components down the line.  Again, it is the quality of the pre-amplifier being used that will make the difference.