It seems you might be located in the United States? if so - and your volume is more than $1,000 a month, a merchant account with an electronic payment gateway (Verisign's Payflow, LinkPoint, Authorizenet.com) is usually better in the long run.
With a merchant account, you will get a virtual terminal, the money is deposited into your checking account usually withing a couple of days after the transaction and your name appears on the consumer credit card statement. And you can capture and process the credit card transaction on your secure website without sending the consumer over to another website
With 2CO, you get your money every two weeks unless your volume is $1,000 a week (which means you should have a merchant account
). Their name appears on the consumer statement as well and you add another company in the middle when accepting credit cards.
Usually with 2CO or a merchant account, as long as the credit card has the Visa / MasterCard logo on it, you should be able to accept the credit card on your website.