If you are in the United States, you should not have a problem with international orders. A United States merchant account provider will look at you - the merchant - when offering you a merchant account. The provider will consider how much you think you will process monthly, what you are selling, and what your average / highest ticket will be. Usually anything under $30,000 for United States merchants will be approved unless the items you are selling are deemed high risk. And the high risk items will vary per provider and the acquiring bank.
If the transactions are rather high was well, this will be considered also. And it would be in your interest to vet the transactions - starting from the basic AVS (address verification service (United States).
Some other ways would be to look at the email address. Is it "free"? If so, that should be a point against them. Make sure the billing address matches the shipping address. If not, another point against them. Call the customer - legitimate consumers will not mind a phone call, some will even appreciate it. (And there are services that will call the customer for you during the checkout process.)