Heat rises so a bottom supply will work best.
One of the most energy efficient water heating methods is the heat pump water heater. This method is proven to be two times more efficient over the standard electric water heater.
Any heater that has the Energy Star label will be very energy efficient. The Honeywell eco line, for instance, are very energy efficient.
The most energy efficient radiator heater is the oil filled one. A better option would be an electrical one because those are almost 100% energy efficient.
The question is better defined as "What the most energy efficient portable heater?" Because one would assume that you will want to be able to take the heater with you when or if you move.
instant gas
Vornado is the brand of heater that is the most energy efficient. If used properly, Vornado heaters can heat just as well as a larger heater, for a much lower cost. They are small, portable, and can heat large rooms. Some of them even have thermostats or timers to increas efficiency.
I have no experience in this, however A. O Smith claims that there brand of gas water heaters are the most efficient. They also offer a hybrid water heater.
Check the code for your area. Most I have seen go through the ceiling.
The Fahrenheat Electric 5120 BTU Baseboard Heater is very energy efficient. Because of its "baseboard" design, it is not necessary to use a powerful to disperse the heat. It uses natural radiance, which saves on electricity costs.
There are many gas pool heaters. Most are efficient and cost less to run than electric heating.
A tankless water heater is much more efficient than a traditional water heater because it only heats the water that is being used instead of heating and reheating water stored in a tank. Rinnai, Rheem, and Bosch all make versions of tankless water heaters that are well-reviewed.
A ceramic heater is going to be your best bet. They are small, use little energy, and actually have a much more powerful output of heat than most heaters.