I have many of the same concerns about credit card companies and big banks that tafan has, and I can tell you what I do:
I do my banking with a local small-town bank that has a very good reputation in the community, and I have a Visa debit card from that bank. And while it is true that Visa pockets a small percentage of each transaction, whether the card is a credit card or a debit card, this is not the major concern that I have with credit card companies.
The major concern I have with credit card companies is that they encourage people to go into debt for frivolous expenses (as I saw first-hand when I was in college, with numerous promotions trying to get me to sign up for credit cards), and then they charge a huge interest rate on that debt, and then harrass people who can’t pay. That’s just not a business model that I want to support.
As far as I know, my bank does not do anything like this. First of all, they do not issue credit cards, to the best of my knowledge. Second, when they do loan money, their interest rates are reasonable, and they don’t loan money to people unless they have good reason to believe that the people are financially capable of paying off the loan. (This protects both the bank and the person taking the loan.)
And when it was time for us to get a mortgage, we got a mortgage directly from this same bank – an in-house mortgage that is actually from the bank, not a mortgage that can be re-sold to someone else. We did this mainly because we like doing business with this bank, but also because we did not qualify for a “standard” mortgage or whatever the term is, since we didn’t have a credit score (because we don’t use credit cards). But that was fine, because the loan we got from the bank was very reasonable, and with a good interest rate.