Preamp under $2,000 used

Cary SLP-98.  There is one on Audiogon right now, with phono stage and a desirable F1 upgrade.  You could probably negotiate very close to $2,000.  You'll be hard pressed to do better for $2k.  I own one (without phono stage) and it's awesome, very musical, very quiet, responds well to tube rolling.

"I am looking for a neutral true to the music sound.."

I may be in the minority here but the main reasons for getting a preamp are multiple inputs, volume control, extra gain, and perhaps more importantly, the "flavor" it could add to the music. If your objective is something true to music which is difficult to measure anyway, you should definitely audition before you buy. I also wouldn't rule out a passive preamp if you can find one to fit into your system. 

If you can find one on the used market, a Don Sachs 6SN7-based preamp should be a consideration.

They don’t come up for sale very often, however. 

I'd look at Audio Research SP-6a's, 6b's, and SP-8's.  Have their caps and critical resistors upgraded to modern high quality ones, and be happy for a long, long time.  This can be done for under $2000, and if you have or plan to add phono gear, these are an even greater bargain as the ARC phono preamps of this era were superb (although MM only).

If you can read (I presume you can), study a bit of electronics and build your own using LM4562 and a few other parts. You will save $2k and build something you can be proud of.