I know they look lovely but woodburning stoves (even modern compliant ones) and fires pump out particulates into homes. I was horrified to see how much - will try and dig out some studies.
Particulates are particularly dreadful for breathing and respiratory system and some are carcinogenic.
I know they are cosy but I wouldn't have one in my house. Especially with children in it.
Using gas for cooking also pumps out more nasties than you might expect.
In the long run, most homes could switch to air or ground source heat pumps. These use a small amount of electricity to extract heat from the ground or air. Solar thermal is also an option where solar panels are used to heat a tank of water during the day that is then used for heating your home in the evening
Yes, they are expensive to buy now (although then very cheap to run) but like solar panels or any other form of technology, they will get cheaper and more efficient over time.
Blocks of flats will likely switch to a centralised heating system using waste heat from power generation (known as combined heat and power plants - the heat is normally wasted by just going up a chimney). Again municipal heating networks are very common in Nordic countries and eastern Europe where the cold has long since encouraged efficiency.
Key to making a success of this will be massively improving insulation in homes - double or triple glazing, insulated plasterboard or external insulating render, insulating floors and roofs to a much higher degree than is normal now. More to Scandinavian levels!
Underfloor heating (the wet kind not electric) works well with heat pumps and solar thermal because the water in it doesn't need to be as hot as in radiators - which blast out heat to reach the other side of the room and so are quite wasteful in comparison
There is some talk about using hydrogen which would use a boiler similar to the way we have a gas boiler today but the technology to captures and store carbon when making hydrogen is not yet at commercial viability so it may not really turn out to be an option. The jury is out on this one.
And yes we really should be aspiring to make oil fired generators and agas a thing of the past! They are bad for the global climate and also really not good for the air quality inside your home.
You can still have an Aga if you like the look of them - electric versions exist.
Your rural idyll will just have solar panels (a small turbine perhaps if you the land!), way more insulation and better windows, a battery and/or solar thermal water tank, heat pump (ground is best if you have a big enough garden but air is fine)
You can watch a fire on a flat screen TV while being in a warm home with no particulates and without pumping more carbon into the atmosphere.
Heating is a massive chunk of our carbon emissions - way more than flying. We have to cut carbon for heating if we are to have any hope of reducing the rise in global temperatures.