Well actually Visa, Mastercard and American Express are just networks that payments are processed through. Amex does issue most of their own cards, but Visa and Mastercard don't issue a single credit card believe it or not. Those are issued through the banks that use their payment networks. What you really want to decide is which bank (and their card) is best to work with since the payment network doesn't really matter.
The grace period on credit cards is usually 20 to 25 days, the time you can go w/o paying interest. But some are shady now and have chopped that down to 10 or 0. However whatever the case that time doesnt start until after a billing cycle closes.
Amex Platinum vs. Centurion - to be honest there's not a huge difference other than the big difference in annual fee. The benefits on the Centurion aren't worth it unless you travel all the time.