It sounds like you're looking for Stripe Checkout (https://stripe.com/en-de/payments/checkout). They handle all the billing portal pages, invoicing, subscription changes and cancellation, etc...

I am not affiliated with them in any way, just a happy customer. I'm actually using it for my side-business SaaS http://panelbear.com/ and saved me days (weeks?) of development work. Happy to help out if you need it.

However, there's a few edge cases that they don't support yet, such as setting the billing cycle anchor to the beginning of the month, and keeping it even if the customer changes the subscription. But I guess it's not a showstopper for a lot of use cases.