Having your site send reliable site email can be a mess to deal with. There is now a new service with a plugin called WP Mail Pro.
The pricing for WP Mail Pro is very reasonable the free plan includes up to 1,000 emails a month, the lite plan includes 10,000 emails a month, the basic plan is up to 50,000 emails a month and if you need to be able to send even more emails from your site then the premium plan includes up to 100,000 emails a month. You can easily change your plan in WP Mail Pro if you need to. The WP Mail Pro services use external SMTP servers so that site email is reliably delivered on your site.
In order to be able to use the plugin on your site you will need to create an account in WP Mail Pro and then find your API key for the plugin settings. In the plugin’s settings, you can set the sending domain that you will be using for the site and then you will need to copy that info and add it as a TXT DNS record on the domain.
The WP Mail Pro plugin also provides features such as logs and metrics. The WP Mail Pro service compares very well with a number of transactional email providers such as SendGrid, MailGun, Amazon SES, and Postmark. The major difference being that the WP Mail Pro plugin setup is very straightforward and makes using it on-site very simple.