I looked at both Netlify and Formspree for the Gatstby Basics Course.
Netlify looks good but you have to use their servers and doesn’t currently really work locally. Formspree is a bit easier to test, but not a fan of some of the features.
I’m going to be showing how to do this with WordPress and native WordPress form plugins in my Gatsby and WordPress course.
However, if you want to do this completely on your own this might help you setup something simple:
https://www.gatsbyjs.org/docs/building-a-contact-form/#run-your-own-server
Integrating with something like Sendgrid might be a better solution.
You’ll want to make sure your hosting for the Gatsby site can run a PHP form handler, and in general switching to a JS driven one might be a better match overall.
Hope that helps a bit!