They will more than likely pull EX. Your scores are higher than mine were when I got approved for my two amex cards. Your income probably wont be an issue either.
If the only baddie is a collections from 2008 and you have at least a year with one of your cards (though some have been approved with less) I'd say you have good chances of getting in.
The charge cards are said to be easier to be approved for and they all have the same UW criteria. If you're going for a charge card, the best one is the PRG (Premier Rewards Gold) for the benefits and signup bonus. The first year AF is waived so after the year you can always downgrade to the Green if you can't justify the AF.
When trying to get in with AMEX I too was worried I wouldn't get approved so I applied for the PRG first, got approved and immediately applied for the EveryDay and also got approved. If you apply for a second card and get denied it should be a SP since you were approved for the first. However, if approved for the second, you'll have two HPs so make sure it's really worth the second pull. I really wanted a charge card and revolver which is why I did both. Make sure you understand fully the cards you're applying for.
Good luck
