If the only thing you're selecting your merchant processor on is a couple of basis points, you're going to end up screwing yourself over regardless. You'll never get the real cost of processing out of a traditional merchant processor regardless - in fact, you really can't unless you know the cards* you'll be charging ahead of time. There's a lot more that also matters, like time to receive funds, reserves, chargeback costs, handling, and dispute resolution, gateway fees, breakdown of authorization versus capture costs... the list goes way on.

* Unless you're doing billions of CC volume per year, in which case that turns into real money.

Not all Visa cards are created equal. Different Visas cost different amounts to process, based on a huge number of factors. Debit/Credit/Charge, Intl/Domestic, Business/Personal, Prepaid, numerous sub-categories, etc.