I drink the bulk of my shakes with milk. I don't drink my shakes in relation to my workouts, I have other things for that. I drink one in the morning to start the day and ease into eating. I drink one or two during the day as a sweet, but healthy snack.
I drink one before bed, and that's the only one that I just use water for, to have some protein overnight. I could still use milk, but that particular shake is thick enough with just water.
I also put in fitness fiber in the day shakes.
As to your suggestion for chocolate milk. There are a lot of people that simply drink that after their workouts, so that's a consideration for you also.