Personally, I'd recommend going against the AA card for the miles. If you're flying as much as you appear to be, you'll earn a rackload of miles just by flying. IMHO, you should maybe go with a hotel company credit card (as hotels are the expensive part when I travel for personal reasons) - you can always cash out miles & find cheap airfare, but not always find cheap good hotels. Either that, or go with some sort of a cash back card to get 1-3% of your company spending back to you. For hotel cards, I'd recommend the SPG Amex or the Marriott Rewards Visa or the Hilton HHonors Amex depending one which hotel chain your planning on going with.

SPG has great hotels & service, but poor choices when it comes to locations unless you're always traveling to major cities, Marriott's got a hotel almost everywhere & great service, and Hilton's got the best mid-tier recognition, IMHO - maybe go with 2 different hotel chains?

As for CC's go with something that will benefit you in the long run. I personally use an Amex Corp. card for travel because I have to - but it sounds like you won't have to do that. Get a card that gives 5% cash back for fuel purchases & fill up all your rental cars on that before returning them to the airport. For air travel & hotels & meals, go with a a hotel card over an airline card if you don't do a cash-back card.

Just my 2 cents on how to maximize your earnings...