Yes. You have it. I would go tank and put r-30 or all my old clothes over it. And a timer. Most are 4500 watt elements. given your light use, and big insulation, you would always have hot water, or at least warm even with a timer.
30 or 40 gallon at true value for about 198 bucks, cant beat that. Could turn the temp WAAY down and forget the timer too.