For self-hosted I use MailIt WP Plugin - But use it with SendLane or similar for best deliverability rates - I wouldn't just attempt to use, for example, shared hosting SMTP server.

I use MailX. It works nice for me. I've heard that MailIt is cool too.

I have recently bought MailZingo, looks fine but in order to use some features like Sequence or Bounce, you need to buy the pro version at 77$ as an upsell.
Currently I am having an issue because it works fine but it does not provide raw html to integrate with landing pages and this is getting me stuck trying to lunch my landing pages created with Instabuilder.
I have opened a ticket with the Instabuilder support and the guys answer onece a day and some of their answer are not that helpfull as we expect.

Mailzingo comes with just one template and buying the pro version you get 10 more templates.

Without the Sequence feature, you can schedule the email to be send sometime in the future.

You can create your lists, campaigns, import from files send unlimited emails, etc.

Hope this could help.
Best Regards
Nestor Silva

Eh; Infinite is free, and frankly, I've been customizing it so much that I'm strongly tempted to simply write my own software from scratch.

Fun fact: I was GetResponse's host in their very early years.