The best anime I saw recently was probably Fate/Zero in every area. The characters, art, music and story were all way above average. But if that doesn’t exactly qualify for 2013, then maybe Monogatari Second Season. I’m a huge fan of the series, so I love that all of Nisio’s work are getting animated.
Character? I’d have to say Kushieda Minori from Toradora.
She has so much heart and guts it puts me to shame.