I am omnivore. The music should be good in his genere^^^. But of course, I have preferences. Nearly in order of my taste (but it changes sometimes):
By orchestration: orchestral, concerto (violin, piano, winds, others), piano solo, organ solo, chamber; rarely other solo, opera, sacred works.
By era: romantics (including from 20th century too), viennese classics, impressionistes, baroque, others 20th c. (R. Strauss, Stravinsky, and so). NOT including all after Khachaturian -- classical music is killed.
By composers: Beethoven (6th!!), Tchaikovsky, Mozart, Grieg, russian Big Fives (Mussorgsky+...), Bach, Schumann, Orff, Vivaldi, Dvořák, Rossini, Strauss family...
By performers: Karajan, Rolla János + Liszt Ferenc Chamber Orchester, Tiffany Poon, Freiburger Barockorchester + cond. Goltz, russian state orchesters + cond. Svetlanov or Rozhdestvensky, cond. Rafael Frühbeck de Burgos, Mari Silje Samuelsen. And many others, of course. Excluding most of actual "big names" -- they only have name, not talent.
By genere: pop, disco, dance, german bigbands of 60s-70s, reggae (only the best! = UB40-style), swing and predecessors, rocks (RR, r.billy, laters), country, jazz (only partially, not typical "jazz for jazz" such "l'art pour l'art"), twist, latins, letkis, some others. NOT including actual, 21st century "music" -- rap, kpop and so on.
By performers: hundreds. Some of them, the VERY best: Elvis, Gigliola Cinquetti, ABBA, Boney M., Enya, Hamburg Audrey [Audrey Landers], Bee Gees, Sandra, Valdor Frank Orchester, Ment Jo Orchester, Shadows, UB40, Arabesque, Middle Of The Road, Luv', Pink Floyd, Tom Jones, Baccara, Ferrante And Teicher, Jive Bunny And The Mastermixers, Queen, Komár László, Pussycat, Chinn+Chapman (Sweet, Suzy Quatro...), Al Bano E Romina Power, Hause Alfred Orchester, Demis Roussos, Neoton, Jill Barber, Ricchi E Poveri, Louis Clark and the Royal Philharmonic Orchestra, Roxette... And there are hundreds of, unfortunately, one-hit wonders, not included above (good example: this set).
^^^= I do not like english distortion of words. Genere, impressionistes and so on, are designedly.