Your first Intent is invalid. The protocol for ACTION_PICK requires you to supply a Uri indicating the collection you are picking from.
What is the best way to let the user choose what app to retrieve the picture from every time?
If you want the user to choose something based on MIME type, use ACTION_GET_CONTENT.
If you have some specific collection (identified by a Uri) that you want the user to pick from, use ACTION_PICK.
In case of a tie, go with ACTION_GET_CONTENT. While ACTION_PICK is not formally deprecated, Dianne Hackborn recommends ACTION_GET_CONTENT.