I recently rewrote my profile page and implemented HTTPS using Amazon S3 and Cloudfront. In my opinion S3 provides one of the easiest and least expensive ways to host a simple, static web site. Unfortunately HTTPS adds complexity, both in what you need to do to build the site and also in how you maintain it.
I did a brief survey and I think that that the simplest way to set up a web site with HTTPS is to host with a service like Bluehost, which provides a free SSL certificate. Bluehosts’s $8.99/month price is reasonable, but not as cheap as Amazon for a really small site like mine, which is a single HTML page.
So, in my opinion with the current push to HTTPS, you are better off going with a service provider that includes HTTPS as part of the service. If you are more technical and willing to fiddle with things, you can save money with S3/Cloudfront.