First time I was late paying AMEX they raised my interest rate north of 25%. They could legally do so, but they were the only card I had that did it so quickly; just one day late.
Discover was my favorite. They had a forgiveness policy and wouldn't raise your rate just because another card did. And their website was very friendly to use.
Their app is blasted easy to use for payments & viewing account information as well. I despise the Chase app where my auto loan sits, as it never loads correctly on my iPhone, or takes drastically longer. Whereas the Discover app and pages load without problem.
I guess that's how they make money and can afford great customer service, which is also something I'm fine with: I couldn't care less what their interest rate is since I'll never ever pay interest. If that's on the agenda, then I'd look somewhere else as you say.
Discover was my favorite. They had a forgiveness policy and wouldn't raise your rate just because another card did. And their website was very friendly to use.