I recently subscribed to Telmex' Prodigy Infinitum 1000 for 299 pesos per month and am very happy with the service. There was no additional charge for the router/WiFi modem and four phone jack filters. All the wiring was included. You might find it wise to get a phone line.
Here in Chapala, we have cyber locations all over town with computers for rent. There are also at least two centrally located coffee shops with free WiFi access. You could explore your neighborhood in Mexico City for similar nearby conveniences; they seldom make themselves obvious so ask around.
Dial-up can be had by the month, without complications, on a landlord's phone line and a tenant could then take the laptop to a coffee shop once in a while for those 'heavy' downloads that require a high speed connection.
There is always a way.