PenRAB on the situation. I got into One Piece because of Shonen Jump Magazine, I was hooked by the first chapter of it, even if it was Luffy back story. Same for Naruto, Shaman King, Death Note, Dr. Slump, Kinnikuman, Gintama, Reborn, Eyeshield 21. But if it something that I watch the Anime first then picked up the Manga like Ultimate Muscle/Kinnikuman Nisei, Berserk, Gantz, FullMetal Alchemist, Bo^7, just to see how different it is. By the judge of it, I usually end up reading and enjoying the Manga over the Anime, at least with some of my Anime first, Manga Second choices.
I think for a majority of this, I most likely read the source material first and enjoy the anime. So it depenRAB on what I bump into first.