There are lots of alternatives, but the central Church of England digital team think that MailChimp is a great tool to get started with managing email lists.
What is MailChimp and why should I be interested?
MailChimp is an email marketing tool that allows you to send mass emails to subscribers. You can design great looking emails and then send them out using the MailChimp system, rather than through you your own email provider.
So if you’re looking to send out regular email communications to people in your church, want them to look great and allow people to manage their own email preferences in line with the General Data Protection Regulation (GDPR) and the Data Protection Act 2018 (DPA 2018)....
...read more here.