Starting a Classical Vinyl Music Collection

Get an ultrasonic LP cleaner for sure.  Even when I clean new records, there is a bunch of vinly chips and dirt at the bottom of the bath when I clean them ultrasonically.

Especially you will need one if you expect to buy any used LPs (which has sometimes worked out great for me, sometimes not).

I don't use a mutl-thousand $$ unit.  I use a generic ultrasonic cleaner and an included LP mount that rotates the LPs through the claning bath.  Chinese units for about $250 incluiding everything.  Works great!

I still cannot believe how quiet the LPs play now. I would say eliminates 99% of snap/crackle/pop.

Check out vintage RCA Living Stereo classical (shaded dog and white dog) and Mercury Living Presence albums.  Recorded by great engineers like Lewis Layton and Robert Fine.  Recent SACDs of these records sound terrific.  Favorites of mine include Saint-Saens SYMPHONY No. 3 by the Boston Symphony/Charles Munch and Rimsky-Korsakov SCHEHERAZADE by Chicago Symphony/Fritz Reiner.  Enjoy!

In my adolescence when I caught the Classical Music bug I listened to the radio a lot and then would explore stuff that struck my fancy.  It should be easier to do this now with streaming, and much harder if one is sticking purely to vinyl as a playback medium. 
  The Music ought to be the first priority, and the playback medium second.  Once. You discover what you like,you can then seek out vinyl editions 

I used the Ultra Sonic $6,499.99 Klaudio Cleaner with poor results.

FYI

"I used the Ultra Sonic $6,499.99 Klaudio Cleaner with poor results"

No RCM will eliminate prior groove damage. If you can't "test play" a used LP, then it's simply  luck of the draw. There are used LP's that can look awful/superficial scuffs  but play fine or LP's that appear perfect and sound terrible. YMMV.

Depending on the stylus  profile, an LP may be noisy on a generic elliptical,yet silent on more advanced. Not always the case, but possible. 

I often find 50-60 year old Classical LP's, use the VERY LOW TECH Spin Clean and they play quite nice. I get those US cleaned and..close to absolute silence.