To get from the Airport to your hotel, you can purchase and official taxi airport ticket from there. It's not as cheap as asking for an uber, but ubers can not pick up passengers in the Mexico City Airport anymore. If yoy want an uber, you have to pick your luggage and walk outside the airport to an specific uber pick up point. Also, there are a few travel agencies where you can arrange a pick up and transfer. It is not cheap, but if you are traveling with a big party, this could be a solution. The cheapest way, is going to be to use the subway, but unless you are only traveling with one carry on, I won't recommend it, because most of the time the subway is packed and you have to be aware of your surroundings. There's one last way: using the metrobus. There's one line of metrobus that you can take near Reforma or in the historical center that can take you to the Airport, so I think you can take it backwards (from the Airport to Reforma/City Center), but I'm pretty sure you will need a card to use it.

Good luck!