Well I think the manga is better. The anime changed around events. Added in scenes that sometimes made no sense. Left out some things - either events, or parts of dialogue. According to fans of Kanda, an Exorcist, the anime made some errors to his character. Cross Marian being my favorite was also messed up in the anime adaptation, where they made him more despicable than his manga counterpart. And it's not the 1st anime adaptation I have seen to be different from the manga. Same thing happened with Elfen Lied and Blood+. The former was horrid, imo. The latter was still decent.
So I would say start with the manga 1st. And read that. It's 221 chapters. But you could catch up very quickly. because chapters only get released every 3 months now. We just got chapter 221 this past week. So we won't have another chapter until late this Apr. Even some people who have read the manga decided to start over when it came back from hiatus.
So I always advise - not just for DGM, but any manga that one start with that. Because it's the original material from the one who created it - the author + their editors. THEN go to the anime adaptations, because things will be different in those and can sometimes contradict the manga.
So I advise keeping the anime and manga separated. Because they're not the same. So no. I don't advise starting with the anime, and finishing with the manga.