This is an open ended question.
For a project like that, first you must divide the project in subcircuits...for instance: remote receiver, logic, output, power supply.
Then you start working on each subcircuit:
Power supply; switcher or linear?
Output; relay or solid state?
Logic; microcontroller or discrete?
Remote; Infrared, RF, other?
Then you start asking questions relevant to each subcircuit, fo instance, if you decide to go the microcontroller approach, you may ask whether to use Atmel, Microchip, etc.