Other cars in the same price category offer Internet connectivity via subscription. So I would expect that. Our Audi has 3G (it's older) and the service is run through t-mobile. The car gets a t-mobile sim and you just pay t-mobile for the service ala carte If you have t-mobile as your main cell phone you can add the car as a connected device for like $10/month or something
I believe Tesla uses AT&T for the service, so I would expect to be able to buy a plan from AT&T. OTA updates and log files are an interesting issue, but I would imagine any internet connectivity required for the car will be included, but you will pay for data for extra stuff like Google maps, web browsers, streaming, etc.