Greatest classical musician?
There've been so many, it's hard to say. However, the late cellist Jacqueline du Pre was pretty amazing.

The greatest composer, of course, is Mozart, though Beethoven and J. S. Bach aren't far behind. Mozart had an amazing level of talent, and produced a vast quantity of fine music during his short life. His compositions are always lively, usually uplifting. They may sometimes lack some of the dark grandeur or deeper meaning found in other composers' works, but the sheer quality more than makes up for it.