I do not think they get to choose what Judge they want.
They can file in different districts ( this is subject to operations but I have seen some shaky reasons to get into different states to file) that show more or less leniency towards whatever the objectives of the Debtors might be based on past precedent and certain trends coming out of that court. (i.e., the SDNY is considered the hardest district by far to get an EC appointed based on past cases , where as Delaware and Texas are considered easier).
Once they get into that district, I believe Judges are assigned, not chosen.