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

since the volume control (THE MASTER!!) has to be before the active gain stage in order to prevent overload. So the noise floor of a tube line stage if well-designed will be a constant. So the noise floor of a tube line stage if well-designed will be a constant.

This is total BS, yes the "Master Volume" is in front of the active gain stage and should be at or around 2-3 o’clock for normal listening, 5 o’clock or nearly full for loud, and 12 o'clock for low listening.
If the active gain stage has a "gain control" as in this case, and has it’s gain increased so then the "Master Volume" is at 9 o’clock for normal, this will increase noise, distortion and whatever other non linear distortions the active stage has, sent to the amp, hence to the speakers.

Cheers George

since the volume control (THE MASTER!!) has to be before the active gain stage in order to prevent overload. So the noise floor of a tube line stage if well-designed will be a constant. So the noise floor of a tube line stage if well-designed will be a constant.

This is total BS, yes the "Master Volume" is in front of the active gain stage and should be at or around 2-3 o’clock for normal listening, 5 o’clock or nearly full for loud, and 12 o’clock for low listening.
If the active gain stage has a "gain control" as in this case, and has it’s gain increased so then the "Master Volume" is at 9 o’clock for normal, this will increase noise, distortion and whatever other non linear distortions the active stage has, sent to the amp, hence to the speakers.

Note: The words THE MASTER!! were added to my post after the fact.
George, your post here is incorrect. Clearly you don’t work with active line sections or you would know that. If anything, turning down the volume will cause the gain stage to have less noise. This is because the input is getting closer and closer to a dead short as the volume control is turned down. And we all know that an active gain stage is at its least noise level with the input shorted...

If you look at most active line sections, the balance and volume controls exist prior to the actual gain stage of the line section. It is very rare for the controls to be anywhere else!

Note: The words THE MASTER!! were added to my post after the fact.

I don’t care when it was added. As the "volume control" is always the "Master", just thought I’d drive it home to you.

Clearly you don’t work with active line sections or you would know that.

Of course I do, don’t be ignorant, if you increase the gain of an active stage you increase not just the signal what’s coming in but everything else including noise, rf ,hum any tube or transistor noise is also amplified when you add more gain to an active stage.

Cheers George

Going direct makes it tough with a turntable. 

Pistha,
I listen to cds and Tidal. I'm back to direct no pre but this time bi amped. Awesome. The AI pre adds quite a bit of bottom.