If you go the WiFi route, consider dropping the Arduino part and connect your sensors straight to the ESP8266. Make your project a lot simpler.
Mobile Internet I suppose is possible - there are various GSM shields and GSM adapters out there, look into them.
I forgot the name, but recently on this forum a long-distance wireless network was mentioned. Covers most of Europe now. Low power, low speed, designed for projects that are installed in remote areas and need to regularly send out sensor data or so. This may be a good solution for your project, much cheaper and better coverage than mobile networks and you probably don't need high speed network connections anyway.