The answers to these questions can vary wildly based on your personal circumstances.

Upfront cost will be a combination of new service installation with RI Energy, and installation of new heating system by a contractor. The grids costs are pretty much fixed, whatever they tell you it will cost to get a meter installation is what it is. The new heating system is where the variability lies.

Dozens of questions like forced hot air or hydronic (baseboard/radiators)? What about hot water? Traditional or modern high efficiency? Home size? Number of zones of heat, etc, etc, add to that the physical limitations of your home for equipment locations, flue terminations, pipe or duct runs etc.

I would expect to pay at least $8k-12k depending on the answers to those questions.

Then there is the savings, is it worth it?

Depends on what your doing now, and what you decide to do in the future. Absolutely impossible to predict actual ROI or anything like that without actual data and decisions on equipment to be installed.

Feel free to ask more specific questions and I am glad to help as I can.

Source: RI Master Plumber who has done hundreds of conversions in the last 20+ years.