Don't forget other greats
Depending on what era you like and what type of compositions you like, there are many options out there
Some of my favorites are Dvorak (landscapes in music)
Chopin (excruciating elegance and emotional turmoil
Shostakovitch (not for the feint of heart - but his Jazz suites are a lot of fun)
Tchaikovsky (the man can get your foot tapping and your heart racing)
Vivaldi (if you like Baroque frivolity)
Grieg (his Piano Concertos are crowd pleasers and his piano works are like songs)
Mendelssohn (at 16 did more for music than most others - and his music has a youthful character which is hard to find)
Sibelius, strong, interesting, acidic. Comes from the colder climes so must be something in the blood
But glad you are dipping into the vast world of classical music - its a rewarding journey!
Oh, just try to get the right recordings, otherwise some of the works can sound dull and uninspired, but that's just me. Gardiner conducting the Beethoven is pure bliss