The site is currently on a surplus server (varela.csail.mit.edu) that works well for the time being and is free, but if it fails in any way, recovery is not guaranteed.
I estimated S3 hosting costs at the highest service level and it comes to about $ $.28 per month for 12G.
Information on hosting web sites on S3: https://aws.amazon.com/blogs/aws/host-your-static-website-on-amazon-s3/
S3 is not the only choice, but we already have an Amazon account so it should be straightforward.