Anime style in "Kill Bill Vol 1"

Just got back from watching "Kill Bill" - highly recommended!

I'm a complete newcomer to the anime scene, having seen and very much
enjoyed "Akira", "Spirited Away", and "Cowboy Bebop".  I really liked
the anime style in "Kill Bill" and would love to get some
recommendations for similar material.  Most of the current TV anime
(DBZ or Yu Gi Oh for example) are very much *not* the kind of work
that I enjoy.  Not slagging them, just not what I like.

Thanks for any pointers - I'm looking to blow a little entertainment
cash in the Anime rack at Best Buy (or do I need to hit the internet
for the quality stuff).

Kendt