I'm actually working on this type of project soon, experimenting with API-based e-commerce solutions and mixing them with static-based websites.
I'd recommend checking out GoCommerce by Netlify. They developed it for Smashing Magazine, who reengineered their website to be static, and use APIs for more dynamic processes (like e-commerce, or user registration). GoCommerce is like CheckoutJS, but simpler. A lot of it is tied into the Netlify API, but I'm sure you could steal some ideas from their setup.
I've also used the WooCommerce API (a Wordpress plugin) in the past to create mobile apps for pre-established shopping sites. It gets the job done and it's documented better than other APIs I've seen. And it doesn't require you to build backend admin interfaces and functionality, you just focus on the frontend app. Between that and the Wordpress API, you have yourself a full fledged user registration/authentication system.
Laravel also works well as a backend framework for payment systems. The Cashier package gives you a simpler API to interface with Stripe and Braintree. And the Passport package makes it dead simple to create a OAuth2 API to securely interface remotely with between the client and server side. Although you'd have to everything up from scratch like checkout flows or coupons.
As you can tell I have an affinity for self-hosted options, so I don't have much experience with the SaaS/PaaS solutions. But once you get these kind of backends deployed on somewhere like Heroku or even AWS, they're easy to manage, scalable, and most importantly cheap.