What is your choice?
I'd probably recommend a DigitalOcean VPS though. Cheap, very stable (had a couple VPS for a year with 100% uptime, as far as I know), stellar support and a lot of new functionality being added lately - block storage, firewall, load balancing. DO is one of the best services I've paid for.
Disclosure: I used to work at IBM about a year ago, in the container service team.
For static content that can be (re)published as needed, I'd use S3 + CloudFront and a scheduled or triggered Lambda that handles the publishing.
https://developers.google.com/apps-script/guides/content has a tiny example where they fetch an RSS feed, transform it, and serve the result.
You also have very easy access to Google services, so you can read from and write to Google spreadsheets, Drive, Gmail, etc.
I've seen the founder setup some impressing services in a matter of minutes.
If your projects are lightweight / low traffic, check out Flynn. You get to push code directly to flynn and skip the docker workflow (push commit to github -> docker builds image -> kubernetes updates pods, this takes time ofcourse). Flynn can also create DB for you.
Or you can just use firebase.
and webtask.io for lambdas, which have a nice free plan (1 req/seq) - this is mostly for personal stuff, haven't tried yet their paid plan.
Formerly Heroku, but now only for toy projects: their approach to pen testing and the insecurity of their Postgres setup count heavily against them, and they're expensive (I keep meaning to write a blog on these points ...)
I've used this method when deploying Hapi.js APIs and need them out quickly.
I love their docker-like CLI.
Most big cloud vendors offer API management through their services.
Digital Ocean VPS for the rest.