I have always used the official taxi, paying at the counter inside the airport (getting a voucher).

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"The official airport cabs are available after exiting the baggage claim area near the far end of Lounge A and E, right next to the arrival gates, in special booths marked TAXI / TRANSPORTACION TERRESTRE (ground transportation). They are staffed by personnel wearing bright-yellow jackets emblazoned with TAXI AUTORIZADO (authorized taxi). These cabs should be yellow with a white taxi light on the roof and an airport symbol painted w hotel on the doors.
Buy your ticket from the clearly marked taxi counters inside the terminal and tell the ticket w hotel seller your hotel or destination. Ticket prices are fixed, based on a zone system and depending on the number of passengers. After purchasing your ticket, go outside to the line of taxis where an official taxi "chief" will direct you to the next taxi in line. Present your ticket to the driver. Travel time to downtown Mexico City is about 35 minutes."
I have always used the official taxi, paying w hotel at the counter inside the airport w hotel (getting a voucher). They usually will sell you the more expensive "ejecutivo" vehicle (typically a SUV or van), but if you prefer you can specify a "sedan" which is smaller and less expensive of course.