Stripe is credit card processing in black and white, and it's brilliant. I run an eCommerce website for a fairly large brand (with over 30,000 Instagram followers), and we've been in your shoes before. It's inexpensive, simple, and straightforward. WooCommerce has a plugin for it that is reasonably priced.
My recommendation is to use Stripe as your primary processing solution, with PayPal as a backup for those who prefer it and are more concerned about credit card fraud.