Lighting Studio Scale Models (in particular the Galactica)

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No short answers I'm afraid. I don't use batteries, only "wall warts: i.e. transformers. For battery power, you have to carefully manage current draw to keep it to an absolute minimum. This adds another layer of complexity.

Everything revolves around knowing how much current your components will draw. This determines not only the power supply, but also the thickness of the wire and the ratings of the various components. Always "de-rate" by making sure any component can handle at least twice as much current/voltage as will ever be encountered in your circuit. This is for safety.

Determine how much each LED draws. Add all this up to find out how much power is needed. Double that to get the minimum power supply.