I really enjoyed Beck: Mongolian Chop Squad. It's weird though, cause the music is certainly the best part of the anime, where as the actual animation wasn't very good & i thought it was paced pretty slow.
The manga, from a story & art perspective, was a whole lot better but lacked what is probably the most important aspect of a story about a band: the music itself.
My advice is to perhaps watch the anime first (which only goes up to the first big festival show) then pick up the manga where the anime leaves off. The manga does go for a lot longer, too. If you watch the credits of the anime, they mention some of Beck's US tour where the manga has all of it fleshed out & quite a bit more after Beck returns from the tour.
And download/buy the soundtrack too, of course. I'v never been the kind of anime/video game fanboy that's ever felt the urge to buy/download a soundtrack, but Beck's songs, brainstorm(Big ****)- has really catchy guitar intro, Spice of Life- Great Bass line, Like a Foojin- I have no idea what Chiba's singing but the song is quite good, By Her(Endless Traveling Map)- Sounds a lot like Rage Against the Machine, & their cover of the Beetles' I've Got A Feeling (Which is not even in the English Dub, I'm assuming for copyright reasons) are all on my I-Pod.
"The Rich are there to take all of the money & pay none of the taxes, the middle class is there to do all the work and pay all the taxes, and the poor are there to scare the crap out of the middle class." -George Carlin