If you wait until you have 6 months of payment history you shouldn't have any trouble getting approved for any of these cards. If you only have one card now I wouldn't hesitate to apply for a couple. Starting the clock on a couple of new accounts now will help you down the road and a couple of inquiries are nothing to be worried about. Personally I never use Discover It and don't really like the rotating category cards. Amex BCE has it's uses but look at Citi Double Cash or Capital One QS for an everyday card. I don't have Barclays so can't comment on that one.
