Hard to say what the best program is because it varies on your circumstances. Living in a major hub I would request flights on that airline. Used to get some pushback that brand X is 50 dollars cheaper but haven’t heard that in several years. Have held upper level status the last few years, upgrade if available and free checked bags which I have pointed would save the checked bag fees when they suggest a different airline. Never got into the credit card game as I prefer my none airline card. Hotels are a different story. Atlas gets rooms in many locations at a discounted rate. Some hotels will not give points for discounted rooms. They’ll have a deal for say 100 nights a month at discount rate. I’ve seen cases when a crew checks in and one pilot is the hundredth night that month so no points. The pilot checking in after them is at the regular rate and gets points.

You are on your own to get to your US gateway for company travel to your base. That being said, some pilots have picked gateways and bases with expensive tickets between the two and been able to point out to the company that a ticket from a foreign location would be cheaper. Just looking at tickets SYD to LAX they’re running around a thousand dollars for the beginning of December so not sure you could find a city pair in the US that’s more than that.