Thanks to Gordon for the reply. Note it's always good to seek simplicity but sometimes it's difficult/impossible to define one single default that satisfies all users. As a quick example if you have a mosaic of multiple image sources, you may always want the most recent to appear on top, but there may be a higher resolution image obscured by something more recent. You can give users the option to choose, and you may also build a composite attribute with a custom definition. Some of our image services use a custom field named "best" that combines other attributes (with a raster function) to decide which is best to show on top.
The mosaic dataset has an attribute called "mosaic method" and if you choose "by attribute" and direct the mosaic to your custom field, you can control which datasets appear on top by default (and if appropriate, allow your users to change from the default). Remember no matter which field you choose (existing fields or something custom), lower numbers take priority (a record with field value =1 will appear on top of a record with value = 2).