Design induction power system and blink led

Hi, I'm actually working on a project where I need to have a magnet moving in front of a coil in order to make electricity for a lighting system. For this system I need to know more about the coil and magnet I need in order to fix the output power. So I need someone to calculate and/or test telling me depending of the power I need, which kind of coil and magnet shoul I use. Also this electricity would be stored ( in a capacitor) to make an LED blink with a frequency and time already fixed. This time set up should also be design ( actullay arduino but would rather use analogic component). Here are quite the easy description I could give on the subject.