I've heard about the new service that Amazon now offers, but I still think that it lacks some major features that MailChimp and others have. I'd recommend you to checkout MailGun, a great service with convenient pricing. What are your sending rates?
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I would definitely recommend going with a SaaS. If you are stranded with the budget then pick the one that has the features that you absolutely need and with the price that you can afford (ignore all the bells and whistles).
@gerdtfhello at my previous job i had some experience with mautic org it is opensource email automation app. Maybe it will help in your case. By the way what are your sending rates?