I learned to play by ear before I learned music theory. For me, that makes sense. After all, children learn to speak before they read and write. The more you understand of music - how harmony and time signatures work, and what chords and inversions are - the more you'll enjoy it.
If you play the guitar, you've got to hold the chords down with one hand while you play with the other, so you're limited to one hand. But the piano is the king of instruments because you have your 10 fingers, which become the 10 members of the orchestra.