I think it will be one of such gateways as PayPal Pro, Braintree, Authorize.Net or 2Checkout.
But I'm stuck and I need your help! Share your experience!
Any pieces of advice will be appreciated!
It would be nicer to elaborate the question in much details. This is very open question as different region will have different preference, different merchant will have different preference etc.
As a developer I would like to use the default payment gateway provided my Magento. This way I do not have to worry about upgrade, customization, installing 3rd party module etc...
Let know if this answer your question or you are looking for something else.
The choice is up to you but I recommend aypal which I personally used: