A Pro PayPal account is by far the easiest way to get set up to take credit and debit cards, as well as direct bank payments from US customers. It is unfortunately pretty expensive compared to a traditional merchant account, but even when you reach the point that a merchant account is neccesary, your local banks should be able to help you. Visa, MasterCard et al are international payment processing brands that almost every bank in the world that offers merchant services can connect you with.
One thing at which you should look very carefully is your exchange rate. PayPal is almost sadistic in how they calculate their currency exchange rates, something I know too well from experience (of accepting payments in foreign currencies, which are then converted to USD to deposit into my account.) You need to make sure your pricing reflects the cost of payment processing, which will include currency exchange. Link hidden: Login to view at PayPal.com can help you get an understanding of the costs and process involved, and when you move to a more traditional merchant account, make sure that your cost of getting from USD to EUR is very clearly explained in any service agreement to which you sign your name.