The TL;DR version is after 4 platforms in 6 years, I've settled happily with MailerLite.
MailerLite is FREE for up to 1,000 subscribers. That means you should be making money form your list before you have to start paying for it.
What You Need
MailerLite has a bit of an approval process. It's easy, but you do need either a completed website or a social media profile. You need to be able to articulate in writing how your business works. Get more details from MailerLite themselves here.
It is also helpful if you have a free incentive to offer your potential subscribers. This can be a PDF book, short story, etc. Give them an irresistible reason to sign up.