I just started this last year and although I'm not sure about the flying to Asia part, the AA cards are the best starting option in my opinion.

Using post #2 , apply for both personals at the same time, get 150K miles, and then 61+ days later apply for the 75K business card and you'll be at an awesome start 225K miles after your spends are complete and you could get to Asia and back in first class (max 67.5K each way) and still have 90K miles!