There are three separate lines for Mickey, Minnie and Goofy. Mickey is by far the most popular, followed by Minnie, then Goofy. In our experience, earlier in the day or late at night are the best times. Be sure to check the opening times on the day of your visit, and be warned that lines can get long, and the DO close the line before the scheduled closing time if the line is too long (unlike in the US where you can enter the line up until the last minute, regardless of how long the line is).
Also BE WARNED that Tokyo Disney Resort continues to enforce it's VERY strict photographing policy, and you will be allowed just ONE photo of your whole group together, with the option of an additional photo for purchase from their own photographer. They take this very seriously, and you WILL get told off and moved along.