Amex uses EX to decision their credit applications, so if you are in the 700s on EX you should be fine.
Are you currently employed?
Amex has a pre-approval feature: https://www304.americanexpress.com/secure/my-special-offers?btct=SJHP_hero_ultimateapply
You enter your name and last 4 of your SSN (be sure that you have the padlock icon and or the address bar turns green to be sure you are using a secure browser) and they will do a soft inquiry to see what you are eligible for. This does not guarantee approval but it can help determine what you are eligible for.
The great thing about Amex is that they backdate subsequent accounts to your original Member Since date. So my advice is to go with Zync because it is easier to qualify for, pay the $25 annual fee and then next year apply for the Blue Cash when you have a better AAoA. Your new Blue will be backdated to 2011 even though it will be opened in 2012.
As far as Blue Cash Preferred being worth the $75 annual fee. Well, I would only recommend it if you spend a lot of money at the grocery store. If you are like most post college aged people, you will probably be best suited for the Blue Cash Everyday with no fee.