It's easier to get approved for one of their charge cards and as opposed to a revolver. The Zync used to be the easiest to get, but since they've discontinued it the consensus seems to be that the Green is their entry level card. Since your scores are in the mid-600s, that would probably be the best Amex card to attempt.

Starting Scores for 2013: EQ 723, TU 735, EX Credit Sesame 751
Current Scores: EQ 733, TU 724 (05/01/2013), EX Credit Sesame 725 (05/08/2013)
Goal Score: 740+ FICO scores
Take the FICO Fitness Challenge Bronze Spade Garden Club Member - Last App: 03/04/2013 - No apps until Fall 2013
Cards: Cap1 Venture 6.4k, Cap1 NHCR MC 750, BankAmericard 1-2-3 Visa Signature - UCF Alumni Association 5k, Discover 4k, Citi Diamond Preferred MC 7.55k, Wells Fargo Rewards Visa 7k, Chase Freedom 5k, Chase Ink 7.5k, Amex Green NPSL, Dillard's Amex 7.5k, JC Penney 4.2k, Kay Jeweler's 5.1k