If you have more than two or three attachments for a feature it would be great to have the ability to sort them based on priority or a standard order. In desktop, they sort alphabetically. On ArcGIS Online, they sort based on order created.
A sort could be determined by adding a field to the attachment table and assigning a value to that field, which would represent priority.
Another thought would be to setup a method to assign attachments to standardized attribute fields - similar to hyperlinks, but with the ease of adding attachments.