I'd recommend trying composers from a variety of eras to see what you like. Too often all classical music seems confusingly lumped together as one entity to the uninitiated and you are likely to have a preference to the style of a certain era.
Try a few key composers from each of the Early/Renaissance/Baroque/Classical/Romantic/20th Century periods.
By doing this I now largely stick with with composers from the late 19th and early 20th Century. I love Debussy, Ravel, Grieg, Bartok, Prokofiev, Vaughan Williams, Delius, Copland, Ives etc.
It's fun to explore the era once you know what sort of thing you like. I personally am not keen on early classical and can't stand the Baroque era eg. Handel, Vivaldi, Bach (apart from maybe his Organ works) etc. All the staccato violins and piercing high pitch trumpet drives me mad.