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

Agree with fsonicsmith re jump factor. 

Answering the OP question, I'd say $5k to $20k. In other words, the price of a Shindo preamp. 

I would rather go straight from DAC to amp using jriver digital volume control than use a $2k preamp. The big jump, where the preamp adds musicality (and not just warmth) happens above $5k. 

Warmth is often just smearing and roll off. Musicality is extra tone, no details smeared away, and extra compelling transients. 

Buy the New Schiit preamp at $699 using 6sn7  tubes, 
justreplace them with the Golden Lions ,and you have the =
to preamps up to 3 timesthe cost, even a solid state option if you choose to  but a Pangea sig, MK-2 power cord. Fantastic for under$900 maxed out .also upgrade the fuse if you choose to.

$5500!

Happy Listening

Find an Ayre K3x with phono. Why waste more money for little gain. Because it is new and fancy, doesn't necessarily mean you will get that exponential gain in listening pleasure.Use your spare cash on something else worthwhile to you. How many enthusiasts have "aging" componentry that cannot be replaced because yesterday's stuff was quality, todays is science and mass market, or hi-brow if you can afford it.

I didn't look through the chain to see if anyone mentioned LDR-based preamps but that is a good place to look especially with a high sensitivity amp like the McCormack.  My three buddies and I have replaced preamps from Eastern Electric, Counterpoint (highly modded), Parasound (JC series), and Slagle with LDR-passed no-gain preamps from Tortuga (various models) or Horneshoppe (the Truth).  In all of our experiences, these are the most transparent pre-amps we have owned with outstanding performance in the frequencies extremes, a gorgeous life-like mid-band, and deep and wide imaging.  For us, these preamps transformed our systems to higher levels then we thought possible and we feel we are no longer limited by our preamps, only by our sources, amps, and speakers.  They are really good at any price level and outstanding killers at their actual prices.  In addition, if you do need a little gain, Tortuga has a buffer that can be added and configured to add a little gain.  I believe both companies offer trial periods and both are owned by colorful, thoughtful people.