New to vinyl - How to get the best out of old classical discs?


I’ve recently added vinyl to my classical listening lineup (mostly piano and chamber music) after realizing how many extraordinary recordings aren’t available in other formats. I wanted to start small, but now that I’m a little more comfortable with the gear and know I like the format, I’m interested in where the biggest improvements can be found. Generic suggestions are always welcome, but there are issues that seem to come up more often with of these old classical discs so if anyone has extensive experience there I would be particularly grateful. My budget is around $1000, and any gear that holds value is preferred.


My current setup:


Prep: Ultrasonic/IPA/detergent, new sleeves, quick wipe with dry swiffer duster before play

TT:  Denon DP-51F

Cart:  Ortofon Red

Phono: Pro-ject Phono Box S2


Then (usually):


MiniDSP

Scott 222C (EL84 PP amplifier)

Klipsch RF-5s (discontinued floorstanders, similar sound to Heritage)


Thanks in advance for any advice!


bluemountain
Replace your Ortofon Red - this is the weak link, get advanced stylus profile for much better frequency response and accuracy. Ortofon Black if you want to stay with same cartridge body and almost the same settings. Or completely different cartridge. 
I would never give up my digital sources, but it only takes a couple recordings to justify the expense in my mind. I play piano and an unknown (to me) Rubinstein or Horowitz recording is a treasure.
Definitely not attached to the Ortofon (or any other part of the system). Some people seem to like Goldring and Denon carts for this type of music, though on paper they look very different.
Genre of music is irrelevant for your cartridge, a good cartridge will play all genres of music equally.
I think a better cartridge and a better phono stage would be the first step.  Perhaps you could find a used phono stage in order to stay in budget.  Something like the EAR 834 would be nice.