Thanks for your question. In my estimation, the safest option of those you've given would be the furnace: in this case, an all-electric furnace that does not use any combustible fuels to produce heat. You would also have the option of either a gas, propane, or oil furnace if you prefer a fuel-burning model. Modern furnaces are very safe and reliable whether they use fuel or electricity to generate heat.
The fireplaces and stoves are going to have open flames burning inside them, and someone will have to open these wood and pellet units up to add more fuel. This will expose the open flames. There are flames inside the fuel-burning furnace, too, but they are enclosed and no one has to get near them to fuel the furnace. The fuel comes in through a natural gas utility connection or from a fuel tank. Fireplaces and stoves must also have a flue for venting smoke from the burning wood. Flues can sometimes get overly hot, and if there are holes or loose connections in the flues, cinders might be able to escape into your home's interior, creating a fire danger.
An all-electric furnace will eliminate the need to have a fuel connection and will get rid of potential dangers associated with burning fuel, such as fires, explosions, or carbon monoxide leaks. Of all the options, the all-electric furnace is probably the safest.
Fireplaces and stoves also tend to heat only one room or area sufficiently; they are usually not able to heat a whole home. Furnaces are designed to heat an entire home, providing warm air wherever there is ductwork to direct it. If you don't have enough ductwork installed to reach every room or area in the house you want to heat, you will have to contact your local HVAC expert to have your ductwork system expanded and more ducts installed.
It is extremely important that the furnace you choose is installed and checked by a licensed, professional installer who is well-trained and experienced in furnace installations. Furnace installation is not a "weekend chore" or a do-it-yourself kind of job. A furnace installed by an HVAC expert will be much safer and will run more efficiently and effectively. In most cases, the HVAC company you purchase the furnace from will also install it. Ask about the installer's credentials and licensing to make sure you have an expert on the job. As in all cases when dealing with HVAC equipment, consult with your local trusted HVAC contractor for more specific answers.
I hope this information has been helpful.