Some business credit cards found on CardRatings.com require only excellent credit; however, there are some that require only "good" credit. "Less than favorable" is ambiguous. Do you mean "good" credit or "poor" credit? If by "less than favorable" you are referring to "good" credit, "good" is also open to interpretation. Some resources consider "good" as any score above 620, although I think in today's economy you really need to add at least 50 points to that to qualify as "good." Others say "good" credit is a score of 700.
The other part of your question deals with using the card abroad. While most countries will accept the major cards regardless of issuer, be aware that credit card companies generally charge a foreign transaction fee every time you use the card. If foreign transactions are a key element of card usage for you, you should shop around for the best rate.
Now, if by "less than favorable" you mean your credit rating is very low, you might want to consider checking out the cards listed under "bad credit." The problem with these cards is they likely carry a higher APR. While they will probably be accepted in foreign countries, as stated above, in addition to the higher APR, you will very likely have to pay foreign transaction fees.
My recommendation is for you to identify which countries you plan to do business with, and when you find an acceptable card, contact the creditor before you get a card to ask about acceptance in those countries. I would also select a card issuer with the largest network in the country where you expect to transact business, especially if you know you'll be traveling there.
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