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

You right, the best preamp is passive, with no amplification, If you power
amp  get  good gain and speakers get enough sensitivity , Take a look
Alexus preamp 

bache
 Take a look
Alexus preamp  

Very nice, a little expensive.$995 
You get the same type of volume control in the $699 Freya from Schitt. Plus you can switch it from passive (as the Alexus is)  to two different active buffer modes with a little gain for some added colourations, tube or solid state. And it has rca and balanced. 
http://www.schiit.com/products/freya 

Cheers George

The $699 Freya from Schitt seems like an amazing bargain for the price.
If I didn't already have something great, and were on a tighter budget, I would definitely be interested.
For passives, the only one remaining that interests me is Townshend’s Allegri+ which uses autotransformers that are wound using Townshend’s own Fractal wire and coated in ultra thin Mu foil. Unfortunately, it does not match my system well since it is single-ended only.

mitch2
  the only one remaining that interests me is Townshend’s Allegri

The Allergri is nice, but being a TVC (transformer volume control) they are coloured, nice but not transparent to the source.
Here is an A/B a member here  Rob_j did between my Lightspeed Attenuator and the Allegri.

https://forum.audiogon.com/posts/77350?highlight=Lightspeed%2BTownshend

Cheers George

Good point George, I haven't tried a preamp made from light dependent resistors yet.  I did try Tortuga Audio's tube buffer as part of their "tour" last year.  It was pretty good and I suspect putting that buffer in-line with their LDR passive would probably sound good, although probably not as neutral as a SS buffer.
I have sometimes thought about constructing a version of NP's B1 buffer but modified to be balanced and to have a high quality attenuator and other high quality parts, but that is actually what my preamp consists of. I have not had a single instance where I used a passive and found it to be the sonic equal of my buffered preamp.