MailChimp
MailChimp is an easy to use mailing tool
MailChimp has triggers that can be very dynamic
One limitation: a subscriber can only be sent a triggered email once, so adds a bit of inflexibility if you want to send them several different emails, each time they submit a form (in our case, an order)
MailChimp does not host a PHP server so if you want to implement custom PHP code, make sure your CMS (content management system) can host a PHP server.