You could use a company like PayEx, NetAxept, DIBS or ePay ( there are many more of cause ). You pay them a flat fee per transaction, I know at least one of them will do it for a fixed monthly fee and $0.04 per transaction. The you need someone to handle the actual merchant account, someone like Teller, SwedBank, Handelsbank ( again there are many more ). Many of these will process VISA and MasterCard for less than 1% of the amount and in some case a lot less.
Stripe is wonderfully simple, but if you want to process any real amount of credit cards they seem really expensive. For quickly starting up I get why you would go with Stripe.