Don't implement the payment processing code yourself. (And using Stripe is _still_ implementing it yourself - they supply only one part of the process.)
Writing this code will take time that you are not using to develop and market your product. (cf opportunity cost). Your code will be buggy. Your code will be weak. Your code will not support the various alternative payment options popular in, say, Holland. (Yes, this is a thing, and it is called iDEAL.) Your code will sooner or later be exposed to a campaign of fraudulent transactions.
Use FastSpring, or your alternative of choice. Yes, it costs more, if you don't put value on your weeks of time to create and support an alternative, and if are comfortable having a weak fraud detection, if any.
When your business becomes successful, when the fees to FastSpring start to dwarf the costs of implementing a payment system yourself, then - perhaps - consider re-doing it yourself.
There are indeed weaknesses in using FastSpring, which after seven years are becoming a pain for me. I'll be writing about that soon. But this is not an issue for a one-person endeavor getting started.