You are closer than you think to having your first AMEX card.
Some things to consider:
Your biggest hurdle (as for any prime issuer) is the number of inquiries weighing on your score. Let them age without incurring new inquiries and your score will bounce back nicely. This will put you in a better position to not only be approved, but to receive a decent SL.
As far what card you should apply for, the Gold Delta SkyMiles Credit Card typically has a decent sign up bonus thoughout the year so plan accordingly. It's not unusual to see 60k or 70k SkyMile bonuses with mininum spend. The card also has a low annual fee ($95) compared to the Platinum or Reserve cards and is waived for your first year.
In general, the co-branded AMEX cards (Delta, Marriott/SPG/Bonvoy, Hilton) have relaxed underwriting (as compared to the core AMEX bank-issued card line) so they are easier to qualify for.
Once you are ready to apply, find a referral link for the card you want - this will generally net you a better sign up bonus than the public offer on the AMEX site. Note: card referrals are a violation of the TOS for MyFico, so please do some research and find a referral from an outside source.
Good luck. We look forward to having you join the AMEX clubhouse. We'll keep your seat at the table waiting for you.