I got hooked on the manga first, thanks to the aforementioned Shonen Jump app. I can highly recommend reading it--the anime's amazing in the way it brings the story to life, but there's a richness to the manga that makes me like it just a tad better. Plus, the manga currently outpaces the anime in terms of material, so there's more to read.
(I haven't seen the movie yet either, funnily enough.)
Also, Yor is best girl. Hands down, no contest. (Except from Sylvia, but we don't get to see as much of her, sadly.)
I'm all for sailing the seven seas, but I've found the apps to have a decent selection at great quality. The few time's I've read fan translations there's always been some level of jankiness that distracts me. Up to you, though.