I think that question depends on where you live and the resources available to you in that area.

What do you mean by efficient? Obviously, minimize the heat loss by superinsulation walls, roof, and windows. Beyond that, a heat pump will use less energy for a given amount of power than anything else. But if you mean cheapest in the short run, then neither of these answers apply because the capitol costs are high.

its nyc area

Is this a new build or a retrofit? Is it an apartment or a free-standing house with lots of land (for a ground-based heat pump)? Nyc area has pretty expensive utilities, but it may also have natural gas - probably the cheapest to use (other than a heat pump).

In Toronto the least expensive of oil/gas/electric is natural gas.

Other options are solar panels and geothermal and I’m sure there are more you could each look into, based on your particular situation

A Nest thermostat can help and will adjust automatically based on a pattern (in winter, we settled on 17.5 at night and 18.5 during the day). You can also adjust remotely, which is a bonus.

Lowering in general can save a lot - our gas company provides comparisons on usage in the neighbourhood and we are now using 70% less gas than others and also helps the environment.

Build with the north, east & west sides of the house encased in a hill or mountain / south side exposure open to the sun.

Insulate well.

Mechanical needs whether fossil gas or electric would be minimal.

Whether NYC or anywhere... most places this design would work well. Unless there is an earthquake or mud slide.

If you don't have a mountain or hillside to build into here is another option. It likely wouldn't be cheap. There's hints why inside the video... (really thick walls)

I will assume when you ask what is the most efficient, you really mean what is the lowest operating cost. Being money efficient and energy efficient don't always mean the same thing.

New York city has high electric rates, and natural gas is available to virtually any existing house. A gas fired boiler if you have radiators or a gas furnace if you want to integrate heating and cooling should be the most economical way to provide heating. If you post your gas and electric rates a calculation can be done if using a heat pump instead of a furnace might be another alternative.

If you are trying to heat a 100 year old brownstone with 11 foot high ceilings the first order of business would be to upgrade the insulation and windows. A professional HVAC company can't explain heating options and operating costs, then I suggest you look for another company.

I don't see above where we know the square footage of your house. That would be helpful.

I would recommend looking at a method/fixture in a wider context, including incentivized energy efficiencies; this will affect operation price and the future value of your home.

-what incentives does your State/municipality offer for heating systems?

-are you able buy into community solar if you aren't able to mount solar panels?

-does your electric utility offer net metering?

-can you install batteries (e.g. Tesla) in a program where the utility can schedule "borrowing" power from those batteries?

-is your home highly efficient in construction and would benefit from an air exchanger (e.g. CERV)?

-does your State offer incentives for specific heating equipment, e.g. mini splits?

IMO outfitting a home newly with gas/oil heat (unless it has hookups already) would create a dinosaur in about 10 years. Climate and the markets are moving quickly towards renewables.

I live in the far north. It can get to -20F. I have no heating (or other electric) costs in winter (or summer!) except for the cost of the meter (i.e. a base fee). I have a super-efficient all-electric mini-home with solar panels (although I could buy into community solar and achieve the same thing), a CERV (which has some heating/cooling capability, but mostly functions for air exchange), and heating/cooling finesse provided by a single, ductless-output, mini-split.

I have as much heat as I want. I never have to worry about the cost of turning up the thermostat.

However, this requires enlightened legislatures and utilities! And I researched and used every possible government-program incentive. The only one I couldn't get was Tesla batteries with electric storage that would be accessible to our electric utility every once in a while. The only reason I couldn't get those was that I don't have enough wall space for the batteries.