Many people find themselves in this situation. Though they've never thought of themselves as "the kind of people who like classical music" (as if this were somehow a separate breed of humanity, "Not people like us, dear"), they suddenly realise (often through movie soundtracks or some other sneaky, underhanded trick) that they really do like it.
So what is a beginner to do? After all, classical music is, within its area, as varied as rock'n'roll or country music. People who like the Sex Pistols don't necessarily like Billy Joel, and, likewise, Holst is quite different from Vivaldi.
Therefore, in the spirit of cautious guidance to the newbie classical music enthusiast, let me offer a few tips. They are completely subjective, I must warn you, and they aren't necessarily exhaustive. However, they are based on a lifetime interest in classical music and in most other types of music (though I will freely admit that country music is not my cup of tea).
If you liked the Star Wars theme, you'll like Gustav Holst's "The Planets",
from which it was plagiarised which inspired it.
If you like heavy metal, chances are you'll like Johann Sebastian Bach, Gustav Holst, Carl Orff, Modest Mussorgsky and Ludwig van Beethoven. Have a look at Richard Wagner, too.
If you like soft instrumental pieces or ballads, you will probably like Antonio Vivaldi, Bedrich Smetana and Frederic Chopin.
If introspective or gloomy music is your style, it is safe to assume that you will like Richard Wagner, Modest Mussorgsky, Gustav Mahler and Edvard Grieg. You will probably also like Tomaso Giovanni Albinoni, particularly the so-called Albinoni Adagio (which isn't really by Albinoni at all - since it is a reconstruction, from a manuscript fragment, of an Albinoni piece, by Milanese musicologist Remo Giazotto
If you're into techno, check out Philip Glass or György Ligeti. You may also find yourself liking Arnold Schönberg and Alban Berg, though these are definitely acquired tastes.
Everyone likes Wolfgang Amadeus Mozart. If you don't, there is probably something wrong with you, requiring therapy.
As I said before, this is completely subjective, and I am sure there are plenty of styles of music not represented here. The intent here is merely to kickstart your interest.
If you feel that your particular taste in modern music is not represented here, feel free to msg me, and I will amend this writeup
to cover your interest, if I can.
Thanks are due to proj2501 and Oneiromancer for suggesting addenda to this list.
For a more extensive list of classical music, by styles and composers, sockpuppet has recently created a fine writeup: Classical Music Starter Guide. Highly recommended for somewhat deeper dives into the fathomless depths of classical music.
Final disclaimer: Make your own decisions. Don't expect my tastes to reflect your own. Go with what you like, and ignore public opinion. Never worry about whether it is "right". Think for yourself. (etc., etc.)
sideways says try mentioning that if you dig industrial, glitch, or drill 'n' bass, you'll dig stravinsky. stravinsky is some good shit. (I couldn't agree more)