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

The only reason for lack of bass, which would also rob warmth, is if the source’s output is "capacitor coupled", and that capacitor is too small.

It’s a simple fix to double the uF (microfarad) of the capacitor and at the same time use a better "quality" one, as most skimp here with average quality industry ones.
 
Myself, all my sources, and everything else is direct coupled, which has the best bass, and no "sound of a capacitor" in the signal path.

I'm sure the source's coupling cap is large enough (I agree that a direct-coupled output can sound better; we use a direct coupled output in our tube preamps).

Output coupling caps are extremely common with many sources. If proper design is applied, a relatively inexpensive electrolytic cap can have performance similar to high quality film capacitor (I realize this statement might be controversial to some; please note the caveat 'proper design').

The problem is that putting a series resistance in the circuit (which happens by turning down the volume in a passive control) effectively raises the output impedance. In turn, this raised impedance must drive a lower resistance (the shunt of the volume control to ground, which is in parallel with the input impedance of the amplifier). When this is done, the output impedance at 20Hz (which is usually higher than the output impedance at 1KHz) is raised also. The combined aspects of the control can thus make the source less able to make bass at the input of the amplifier.

This is easily heard.

Installing a larger coupling cap is often impractical! A larger cap might also induce low frequency instability in the source, depending on its design. It will certainly introduce additional coloration, due to the additional inductance since capacitors are wound in layers, and you need more layers to create a larger capacitance. 

Reducing the value of the control can reduce the timing constant problem, but can also pose a problem for some sources. The bottom line is that you have to try it and see, while also comparing to a competent active preamp. 

The combined aspects of the control can thus make the source less able to make bass at the input of the amplifier.

This is not correct in this case, as with most of today's systems with low output impedance and high input impedance. 

If the source is low in impedance and in this case it is at 100ohms.

And the amp has high input impedance and in this case it is at 100kohm.

It doesn't matter one iota where the volume control is positioned here, these figures have a perfect impedance match regardless of volume position. As do 90% of sources and amps out there when mated to 10kohm passive volume controls. 

So the only reason for a lack of bass in this case (if correct) is a coupling cap that's too small, and that 100ohms source output impedance is rising at low frequencies which "would" roll off the bass.


Cheers George

It doesn't matter one iota where the volume control is positioned here, these figures have a perfect impedance match regardless of volume position. As do 90% of sources and amps out there when mated to 10kohm passive volume controls.

This statement is false. Its not wise to assume that 90% of all sources can drive a 10K load.

The position of the control does affect the sound in many cases (although most people don't get to find this out because if a digital source is used, the output will likely be clipping the amp). So an audition with something like a tuner that makes less voltage and so won't clip the amp will reveal the issue.

Audition is the bottom line- if everything is set up correctly, a passive will work fine.

So the only reason for a lack of bass in this case (if correct) is a coupling cap that's too small, and that 100ohms source output impedance is rising at low frequencies which "would" roll off the bass.

This conclusion is based on a false assumption, and so is also false. Its highly unlikely that so many sources would have a coupling cap at the output that is too small.

Its not wise to assume that 90% of all sources can drive a 10K load.

This is picking hairs and scare mongering, and just selecting a worst case scenario. 

90% of amps are 33kohm input impedance or higher. 

Very rarely is an amp a pitiful <10kohm, which even many tube preamps won't drive let alone passives.
In fact most amps are >33kohm or higher to 100kohm or more. The loose industry standard input impedance has always been 47kohm, though it's not adhered to. 
  
So the impedance ratio of those 90% of amps regardless of volume position with a 10kohm passive will always be better than the industry regarded minimum ratio of 1:10 source to passive for the input, or 10:1 minimum for the output, passive to amp.
 
And with the voltage of most of today's sources again are higher at >2v,  and the input sensitivity of most amps are <1.5v, the only thing that could "clip" is the amp with too much volume from the passive volume control, so more gain from an active is not needed, in fact it's a curse as then the volume control can only be used right down low in many cases.

Actives are not needed unless you have an amp that is 10kohm or less and/or it's input sensitivity voltage is higher than the source volt can give out.
  
Or the other contentious reason to use an active pre is, if you like the colouration of active preamp, to me it's a bit of a ban-aid fix for something else that's not right better to fix it, as no active preamp sounds like the proverbial "a straight piece of wire" only direct source to amp can do this or second in line a passive volume control.    

Cheers George