Implementing an Online Payment System

We have had an online payment system approved by our bank and are looking to implement it into our website to accept credit card payments.

I understand I can either have a link to a secure site away from our wordpress site or otherwise we can use the API provided by the bank to implement the payment system into our website.

Is there any advice out there on how to achieve this? From my research it appears I need to use a plugin but is there a highly recommended plugin to use and what are the steps to implementing it?

Thanks for your help, I have never done anything like this before.