We used to have Delonghi oil filled rads. Being electric they are expensive to run but they are fitted with a thermostat and timer so if correctly set costs could be kept to a minimum.
All electricity consumed by a heater gets converted into heat (apart from any used to drive a fan around - which is small), so there is no difference from an efficiency point of view between different types of electric heaters.
Night storage heaters merely take their electricity at a time when it costs less.