What should I consider while designing a power supply for a device?
I'll answer this in terms of what specifications should you nail down before you get started with the design. I'm sure I'll forget something, and there will always be a special situation that introduces new requirements, but to get started:


What is the output voltage and current requirement?
What is the input voltage; is it ac or dc; is it stable or varying?
What is the required isolation between input and output?
What is the maximum cost for the supply?
What is the maximum size (volume or board area)?
What is the available cooling (forced air or convection)?
What is the required ambient operating temperature range?
Do you need a slow-start feature?
Do you need over-current protection?
Do you need over-temperature protection?
Do you need any kind of external enable/disable/reset control?


For ac-input supplies:


What are the local safety regulations?
How variable is the local mains voltage?
What is the required fuse?
What are the required separations for wires connected to mains from other wires?
Do you need inrush current limiting?
Do you need power factor correction?