2001 I first started listening to J-Pop and I heard of two artists Ayu and Hikki. So I listened to Dearest and Final Distance. I felt that Ayus song touched me more. So then and there I downloaded every song she released so far. And then realized Ayu is the one for me. I never connected to Hikkis music like I did with Ayus. But I still like her and think she's very talented and a very good singer. My favourites are the already mentioned
Final Distance,
Automatic and the complete
Heart Station album. (Minus Boku wa Kuma)
First Love is also a classic song - but probably not what you're looking for.
