When you say you want an account that supports european business - do you mean an account that allows you accept foreign charges from Europe? Or an account that lets you accept in Euros as the currency?
Also - are you a U.S. based or non-U.S. merchant? If the latter, your choices are a bit more limited in most cases. If you are U.S. based, then you will probably want to look for a smaller merchant processor that can give you more personalized service as you are describing.
Definitely check into everything... references, track record, any "fine print" in the contract like termination fees, contract length, full rates & fees (and watch for fees under different names!) and make sure to verify - in writing - everything that you need so that both parties have a clear understanding.
Best of luck with your search for the right merchant processor for your needs!