I wish there were better advise but after years of e-commerce experience all anyone will ever tell you is don't use Stripe. Don't use Square,don't use PayPal. Don't use any of the faceless companies for anything remotely critical and for anything that is critical have two backups. Basically that goes for things like hosting, payment processor or anything else your business depends on.
A bank! All the banks offer merchant accounts and will have gateways they are setup with. Authorize.net is the big gateway if you want to do heavier coding and integration with existing solutions but there are hundreds of thousands of options. Regional banks usually offer the best rates. But this is if you are a "real" business. E-proccessors like Stripe, Square, PayPal etc are going after the very low hanging fruit of what are essentially consumers more so than businesses.
