You will probably want to use policies for things like deleting items in the "Deleted Items" folder and purging inboxes for accounts that not regularly managed by a user.

To create a policy for deleting items, you will need to go to Organization Configuration > Mailbox > Deleted Items, then right click and create New Managed Content Settings. For length of retention, I chose 2 days, then keep default for Retention period starts and change action to "Permanently Delete."  Then you have to adjust the mailbox database properties and go to Limits and adjust "Deletion settings" > Keep deleted items for (days).  This number of days is the number of days that users can recover items even after they are removed from their Deleted Items folder.  I chose this for 2 days as well.

After creating the Deleted content settings, then you can create a "Deleted" under Managed Folder Mailbox Policies.  Link this policy to the content settings that you just created.

Repeat the procedure for create a policy to auto-delete items for Inbox.

After creating these policies, you can choose when to run these policies – i.e. daily at 3am.