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

Most sources have output stages the equal of preamps today, except for wimpy capacitor coupled tube ones.

Cheers George

“No preamp” is a straight wire. It will add no noise, no distortion, and in 99.9% of cases no frequency response anomalies.

There is not a preamp made that has the same characterics. Thus, there is no amount of money that can be spent on a preamp that will sound better that a straight wire.

There are reasons someone might prefer a preamp to a plain interconnect. These include gain, impedance matching, and pleasurable distortion.

Personally, I have retired my preamps (I have three to choose from) and have my DAC connected directly to my amplifier. It is better. 

Hi OP

The gain control is varying the tube's circuit gain.  The volume control varies the level of the input signal.  They are completely different animals.

You can just put the gain control at some random point like 3:00, but is that the optimal point?  Not clear.  One would need to know a lot about the circuit design to make that call.  I'm not surprised AI isn't getting involved in the answer, as it can be quite complicated.  It's also why few amplifiers actually have gain controls (except for vintage ones, and that was because of the wide variety of speaker efficiencies back then).  

My suggestion is that you try a range of settings.  There is likely to be one spot you prefer for a 'given volume level.'  Most gain circuits have a sweet spot.  It will still work outside of that range (since they made it available to you to adjust) but it won't necessarily work as well (e.g., less linear).

What I do is listen one night with it turned all the way up.  Then the next listening session, turn it most of the way down.  Use the volume control to set the music at about the same level for both sessions.  Then try turning it to the midpoint, then vary from there, etc.  Trying the two extremes first will help you "frame" a reference point to fine tune the setting.  My MC240 clearly sounds its best between 1:30 and 2:00, but your results could be completely different.

Replace your amplifiers with a wire and let me know how that works out for you.

Since I listen to speakers, my DAC doesn’t have enough current output to make much noise, so I think I’ll keep my amplifiers (my speakers are bi-amped). My preamp wasn’t doing anything useful, as the DAC has enough output to drive the amps and the speakers to 100+ dB peaks.  The preamp was only adding noise, distortion, and frequency changes.