The manga is definitely more thorough. I was able to get the names down of all of the characters before I finished the first manga, so it's probably better that you'd read the manga also. I usually don't watch the anime until after I've read the manga because it's usually not quite as good, and they leave out so much stuff that sometimes it can just be really confusing to even be watching it without reading at least the first volume or two of the manga first. I figure it's a lot like going to see the Harry Potter movies without reading the books. You may think you understand what's going on, but there's a lot of stuff behind the scenes that the movie won't touch on but the book goes through in it's entirity.