I worked a number of months in Mexico City. I would not recommend using the subway. I would stick to hotel taxis (Turistico) cabs or the licensed yellow airport cabs.
In regards to safety it is a scary place at times. I was lucky and had no issues. One of my employees who grew up in Peru who was also working with me and speaks fluent Spanish was mugged twice. The first time they tried to kidnap him; he fought it off and instead they robbed him. The second time he was shopping in the market with his wife that he had brought to Mexico City for the weekend. 3 guys ran up to him - one pulled a knife, one grabbed him from behind and restrained his arms, the other put his hands in his pockets and took his money, watch, cell phone, and wallet.
All I can say is be careful.