Hi Brad -
One pitfall many have fallen into is to sign up for too many cards and not be able to make the spending limits.
Million Mile Secrets suggested some excellent cards, however based on your spending habits there's no way you'd hit the spending on all those cards at once.
Personally I'd apply for the two AA cards first (based on your spending limits I believe you could hit both of those), and once you hit the spending limits apply for the Sapphire if it's still available.