Beck is such a unique anime, in terms of art style, it's hard to find recommendations that really compliment this series well. Of course, there will always be out-there series such as FLCL and Paradise Kiss that have similarly distinctive styles that don't follow mainstream anime, which are perfect for your watch list. Thankfully, there are tons of anime series that have to deal with music and characters growing from it.
Shows like K-On! and Kids on the Slope are excellent series that have everything to do with music touching the hearts of the main character. Just like with Koyuki's change in personality after reconnecting with music, the characters of these shows have found a life's purpose hidden in notes and instruments. In addition to shows that revolve around music, beloved series like Angel Beats! make a perfect follow up to Beck for the pure reason that both series have a huge emotional impact.
If you like lists that look beyond the general premise of a show, we've found a wide variety of series that will definitely make your watch list. Vote up for your favorite series and let us know which ones you would have liked to see!