Something to ponder: "No annual fee," "points, miles, etc." are all paid for by late charges and penalty fees. Banks that offer those things also actively try to trap people, in order to generate big fees. Do you really want to do business with a company like that? In any case, many "no fee" cards will suddenly gain fees next year, as new consumer protection laws take effect - if anybody enforces them.
BTW: Many years ago, I sometimes had trouble paying hotel and rental car bills with a debit card, but over the last 15 or 20 years, there has been no problem.
(The one situation where a credit card (with a deep limit) turns out to be handy is chartering a boat - you can choose to "charge" a large damage deposit - later refunded - OR purchase insurance for a small non-refundable fee.)