That's very good news p51, and thanks for keeping us updated about your approval. Now you will have to use responsibly and pay charges made on the card in full each month, so that you will have some good history with Amex.
It is usually wise not to keep cards with unnecessary fees (especially high fees) to save money. You might be thinking of getting your deposit back and no longer pay for that card, so you could choose to close it eventually.
Honestly, I can't tell what will happen to your score if you close the secured card right away, since that is your only revolving account now. Closing the card means you cut that available credit away while your Amex charge account does not factor into utilization and available credit. I would like anyone who has knowledge about this to clarify and correct me if I ever made any mistake, and this is something I need to learn.
But nothing is wrong when you use credit responsibly. A charge card with good history should have positive effect on your credit profile.
As of your credit history, it is not a concern, as the closed account stays on the report for 10 years, and AAoA will not decrease due to the closure. If you don't want to waste money on that secured card, then you can certainly close it.
What I would do in this situation is to see when the annual fee on the secured card is due. If you would like to apply for another revolver soon and the secured annual fee is due some months after today, there is not much harm if you keep it for a while and close it right after you get a new revolver. This takes some extra effort as you have to monitor it for fraud, but an open revolving account might help a little bit with getting approved for another, just in case.
However, you are never required to keep the secured card after another revolver. Keeping the secured card might simplify new application, but it wouldn't be too hard if you don't. For the sake of money you can always close it at any time, especially if you need the deposit back and/or don't want to pay annual fee for another year. Shouldn't affect your ability to get another revolving account if you close it now.