Mushishi
Mahou Shoujo Madoka Magica
Gundam SEED
Stellvia
Full Metal Alchemist
Kaiji
Hikaru no Go
Baccano!
Most of them captivates you within the first episodes. Gundam SEED and Kaiji are probably closest to what you're actually looking for, but since you're new you you don't actually know what you're looking for, and I bet you would probably like the rest too
.