Ignore your kids. Follow signs for "ground transportation" which includes "taxis". I see no reason why cash is better, but ask for a receipt whatever you do, for your own safety (not that I ever do that, actually.) Don't forget to tip between $15-20, depending on how nice you think your cab driver is (they're generally a bit silent or surly, but if they help you with the luggage both ways, that's worth an extra dollar or 2.)
Since it's a flat price, the driver is incentivized to take the most efficient route, but if you feel better about it, you can check yourself on your own GPS app on your phone, as they go. Have both your exact address where you're going, and it is also helpful to say "44th between 6th and 7th" (that is, the street and the avenues that it is between) which you can see by looking at a map.
I understand why sometimes it's easier to have a driver waiting. But it's a big airport and finding the driver is harder than just taking a cab, and paying extra for meet and greet isn't worth it.