Before implementing my own Mailgun module for Magento 2 I have tried some alternatives.
1. andelux/mailgun-magento2
github.com/andelux/mailgun-magento2
It just does not work for me: I have got a lot of PHP errors.
It looks like the extension is built for an outdated Magento 2 versions despite the last commit was just 2 months ago.
Maybe the developer does not test his extension with all Magento 2 versions?