I got started with the anime. Never saw it on TV or dubbed, but I went looking for it online to watch when I learned my favorite Japanese voice actor did Ginji's voice. So of course, Ginji is my favorite character, but I love all the characters after watching the show over and over again!
There are definitely some great interactions in that show, lol!
Since there wasn't enough of the anime (45 episodes was too short!) I started reading the manga. I won't say I like it better than the anime, but I like it at least as much, and it definitely fills out the story more -- at length!
I like it when anime and manga are a bit different, too, as it makes it feel like I'm getting two for the price of one or something.
And of course, the manga actually finishes the story (eventually) so that is (or will be) very satisfying.