We use 2checkout. As far as I know they accept many of the major ones. The only downside with them is that their fees are very big compared to other payment processors.
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Likewise, my business has a regular debit card, but as far as business credit cards go, I never saw real benefits in them for me. Maybe it is because my business is too small, maybe the expenses do not warrant having a credit card, maybe I am just not in the field of business that would naturally use credit, like bakeries, restaurants, etc.
Business credit cards are costly, yet there are so many personal credit cards that not only won't cost you anything, but can earn benefits at the same time.
I personally use Visa Debit Card, perhaps due to Verified by Visa security measure that enhances the security.
The thing is I have been allocated a 8 digit passcode and whenever I try to make purchase, it randomly asks me 3 of them.
(eg. 1st 5th 8th)