I'll have a go...
The places I've lived the choice was between VTR and Telefonica. The consensus seems to be VTR really sux. The Admin could tell you about that. They've been OK for me but I've never had to call them with a problem so I consider myself lucky. I've asked a few people and they tell me Telefonica is better.
TelMex seems to be an alternative that is pitched as an Internet
business solution, but the idea of the Mexican phone company as an alternative.....
I think there are other companies? But those are the biggies.
I don't know the download limits etc. Or if there is one?
Hard to get connected? If you rent a place in your name on a tourist visa, yes. You'll have to have Internet in someone elses name, who is not on a tourist visa. In all the places I've lived, (except one) the owner already had Internet in their name, (they were paying the bill) and charged me for Internet as part of gastos communos.
Yep, you can rent a house or apt on a tourist visa but you can't contract for Internet in your name.
IFAIK, No, you don't need a phone connection. Most people have mobile phones anyway, not landlines.
Income. Not a problem. You won't be able to contract for Internet on a tourist visa anyway. So the 'problem' is getting a place that already has an Internet connection and convincing the owner to rent to you.
Sorry if this is confusing.
Yes you will be able to get Internet.