AWS Lightsail Malware Cleanup & Hardening

My corporate site runs on an Nginx + Node.js stack inside an Amazon Lightsail instance. It has suddenly gone offline and the behavior suggests a malware compromise rather than a simple configuration error... (Budget: $30 - $250 USD, Jobs: Amazon Web Services, Cloud Security, Linux, Network Security, Nginx, Node.js, Security, System Administration, Ubuntu, Web Security)