My personal favorite case of choice is an old Altoids Tin. No matter what you're using to hold the project in, now is a good time to see if everything fits and that it still works fine.
Mine fit perfectly into the tin case. After hooking up some headphones everything seemed to work fine, including the LED.
This is also a good time to design your internal layout and decide if you have enough room to put the solar cells on the inside or not.