Online credit and processing/merchant accounts

We use a company called Shift4 as our payment gateway and are happy with them. They integrate with pretty much every banking network.

Credit Card Payment Gateway - Fast, Reliable, and Secure Credit, Debit, Check, and Gift Card Processing with Tokenization | Shift4


Again, don't know if it's a fit for you or what your exact requirements are but it's another option. We use them because they integrate with our web host, and our gift card provider.

Keep in mind that usually a payment gateway is another middle man that forwards the online CC info to your payment processor (let's say Chase/Paymentech or First Data) who then takes over with getting the authorization taken care of and getting the money into your bank account.

I'm sure godaddy is attempting to be that middle man for you with their all in one setup.