The problem starts always where you want to accept credit card payments for your business. There are Visa and MasterCard regulations that bind your company to a certain Visa/MC region.
That means, if you are a US company then you need a US merchant account say with authorize.net it is not possible to apply for an account in Europe!
So to start with you will need to be clear where your customers are coming from and where it would strtegily best to place your offshore company, then (and before you setup a company) you will need to figure out what options you are left with in regards to accept credit cards online.
You can forget about Seychelles and Belize! Most often as you may have read here already, people are looking into BVI, Malta, Cyprus and the UK. BVI is too complicated to setup and I would not recommend you to go that route.
On a side note, you can forget about privacy if you are looking for a merchant account in a real setup, it will not work.