I have deployed solutions for couple of clients who are sending 1 million emails/months using AWS SES and sendy. It's reliable and very easy to setup. Sendy gives you a way to manage mailing list and schedule campaigns, compose templates and test them. It gives the visualization of the campaign as well. One issue with Sendy is you can't have multiple users maintaining the same account. You can integrate SES with your existing wordpress site as well.

Checkout mailgun as well. It's cheaper solution.