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

I am actually quite pleased with what can be found on CDs of older performances, at least if you are willing to buy the CDs used.  There are not too many performances only available on the original vinyl.  I tend to do most of my classical listening via CDs because noise is particularly intrusive with classical music because of the extreme dynamic range and because I collect a lot of modern performances that were never issued on vinyl.  At least modern recordings of classical music sound good and have not bee subject to horrible mastering as is the case with popular music these days.  Also, some digital reissues of certain labels actually sound better than the original vinyl issue (such as 1970's DG).

The first thing I would look at is your choice of phono stage.  It has been quite a while since I heard the Pro-ject phono stage (so it might have been improved), but, I thought it was not very good and I actually liked their low-priced solid state model much more (and I use tubes in everything except my music server).  I 

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.