The best option is to use MailChimp to manage your subscriber lists and also to send the emails. There are plugins that can integrate with your MailChimp account but even that is unnecessary if all you want is to add email addresses and then send emails when you write a new blog post. The way it works is MailChimp will check your RSS feed every day for new posts and when one is found it will automatically send it to everyone on your list.
MailChimp is very powerful and easy to use. Here are some articles that will help you get started.
The next best option is to use the Subscription feature that’s part of the JetPack plugin. You will need a WordPress.com account to use it but it’s very easy to sign up for one. The plugin will guide you through the process. Click this lovely link to read more about JetPack Subscriptions