Can I only send status update emails for select job statuses?

There is an email notification entitled "Order Status Change."  This email notification is disabled by default - i.e. it has no recipients assigned to it.  You can enable this notification by edit this email notification to add recipients.  Once enabled the email notification is sent out for every status change associated with the order.  The only exception to this would be if the product uses a custom workflow AND you leave the external stage meaning blank for that particular stage, then no email notification will be sent when that particular stage is selected.  Note that if the external stage meaning is left blank, then when the user views the order in their order history the status will also be blank.
Setting up the custom workflow:
To set up a custom workflow, you will need to go to Preferences > Workflows and choose "Create New Workflow".  You will need to first give the new workflow a name and add any applicable instructions before clicking "Save".  Then you will need to create a stage for each valid step in the workflow.  For each step, you will need to define what the "Internal Stage Name" is for each step.  The Internal Stage Name will be what you will see as an admin when you are processing orders.  If you would like the customer to see an alternate name for that stage, you can modify the "External Stage Name" - what the site user will see in their order history.  You can also choose to leave the External Stage Name blank.  Once you have created all of these steps, you will need to define that the product will use the new workflow by editing the product in Sites > [Site Name] > Products > [Product Name] > General tab in the "Order Management Section" and choosing the workflow from the setting "Order Status Workflow."
Customizing the email notification:
Go to Sites > [site name] > Email Notifications and select the "Order Status Change" email notification.  Click "Customize this message."  Change the recipients of the message by clicking on any of the options in the "Users" box and then clicking on the arrow pointing to the right.  You will see that the user is added to the "Who receives this notification" box.  Click "Save Changes." 
Note that custom workflows and custom email notifications are advanced features not available with the Pressero Standard plan.