Open up the Google Contacts app on Android. Go to the desired contact (do not edit the contact). Long press the phone number you want to set as the default number. You should get a pop-up dialog with Copy, Edit before calling, and (Tada!) Set default.
You can do the same thing with email addresses.
This works with the official Google Contacts app from the Google Play Store. If it doesn't work on your phone, make sure you are using the official app and not a phone vendor-supplied version (Samsung, LG, etc.)
This works in Contacts Version 6.01 that was installed on my phone by Motorola and Version 2.5.4... from the Play Store.