To be honest, if it's a static site and you just need a little bit of compute... Cloudfront in front of S3 and lambda is probably the cheapest way to give someone a basic website (just a contact form and nothing else)
It's easy to develop for, it's easy to automate deployments, I don't have to worry about keeping anything up to date, and I can just focus on the small amount of code I want to write.
The most expensive thing is the Route 53 configuration at $0.50/month/domain.