You can tick the box that says guests must go through verification - but you can't choose what type of verification (Reservation Requirements).
You can of course ask for additonal items at check in, but you must make this clear to guests before they book both in your description and your email exchange.
You should note that doing so is still no guarantee of past or future behaviour.
And there is absolutely no value in taking a person's credit card number as you cannot do anything with it. You can't charge against it or use it in anyway as it is considered fraud. Passport and/or drivers licence will at least tell you the person who turns up is who they say they are (in most cases!)