My first series was-- tragically-- the original English One Piece dub.
I got hopelessly committed and read through 400 manga chapters in a week (not being employed at the time helped
)
Other series which stuck to me:
Eyeshield 21 (Somehow, manga makes American football better than it actually is IRL)
Great Teacher Onizuka (over the top all to often, and the official version has truly awful typesetting)
I found the Korean manhwa they stealthily tried to pass as manga during the height of the craze are often surprisingly good. From there, my favourites are Rebirth and Priest, neither of which gets a satisfying conclusion if you follow the English translation (the translator of one went bust after 23 volumes, the author abandoned the other after 16)
In terms of animation, Soul Eater is an excellent 50-episode series sadly ruined by being a 52-episode series with a lame feel-good ending. Black Butler (Kuro****suji) also has similar problems with weak end-of-series delivery (too much ex machina stuff, missing payout) but really entertaining characters.
Gurren Lagann is good in small doses for the 'makes you have some faith in mankind'.
I've been working through Fullmetal Alchemist: Brotherhood, and it definitely has the trillion-yen production values, but I'm not sure how it will let me down.
Also, if you like sophisticated animation, America did do a couple decent series-- Gargoyles for one.