This is an open-ended question to pull together information as folk develop more options. The below answer is based on snips from https://chat.civicrm.org/civicrm/pl/4refrsqotib9tf9gyrscffk8my
In response to a question about WP, Caldera and iATS play nicely and do recurring
no, it's either of these two add-ons as of now stripe and authorize. iATS isn't an option for payment processors so it would need to be developed likely.
the official CF payment add-ons support PayPal Express and Pro, Authorize.net, Dwolla, Stripe, Braintree, and PayFast gateways.
As @danaskallman mentioned CFC integrates with Stripe and Authorize, with integrates I mean that it calculates/updates the payment fees and transaction ids, etc.
And recurring contributions are not currently integrated/supported.
we developed a Caldera payment processor for eWAY Rapid API (eWAY payment gateway) - this hasn't been published OSS yet.
Can confirm, Caldera CiviCRM is missing recurring contribution feature.