Getting Mandrill set up for Ghost is quite straight forward. In your config.js, just make sure to have the following snippet under the Production section:

mail: {
	transport: 'SMTP',
	host: 'smtp.mandrillapp.com',
	options: {
		service: 'Mandrill',
		auth: {
			user: 'USERNAME',
			pass: 'API KEY'
        }
    }
}

It's nearly identical to how the Ghost docs asks you to set up Mailgun but with the extra definition of Mandrill's mail server.