I don't know much about React but Gatsby should be nice; although I had trouble with managing Contents in the past, so I eventually recommend some CMS. I think WordPress can also expose the API.
IMO, though, in Gatsby, you have to create your own building blocks a lot; unlike Jekyll.
Deployment
Netlify can handle quite well with static website, without offering to much.
If you need some minimal serverless API, I would go with Now.sh
I think Now.sh has very nice Next.js support.
Heroku supports all kinds of server, but the starting price beyond free tier is a little pricey.
For Docker, I prefer to deploy on Google Cloud Run; but that is if you need a real server.
Reality
Today, I have just used Nuxt with my custom CMS (build with Fastify and Typegoose), deploy on Google App Engine. I like Nuxt for simplifying routing, and doesn't force me to use GraphQL.
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Deployment
Reality
Today, I have just used Nuxt with my custom CMS (build with Fastify and Typegoose), deploy on Google App Engine. I like Nuxt for simplifying routing, and doesn't force me to use GraphQL.