Hello: Question one… You need to compare delivered energy costs. Multiply the btu content of the energy by the energy factor of the heater, (roughly .90 for electric and .60 for gas) to see how many btus you get per dollar. Size of tank depends on your maximum hourly need. You’ll get 70 or 75% of the volume of the tank as undiluted hot water.
Question two… Really good insulation on a tank will negate any need for a clock unless you have time of day metering.
Question three… Most recirculation simply trades saving water for increased energy use. The Metlund system pumps only on demand, greatly cutting waste. There are various Metlund look alikes out there. If the house is not too spread out, consider a manifold plumbing system… good potential for savings and fairly quick water delivery.
The unasked question four… How about installing a GFX shower heat exchanger? Great idea! It can recapture 60% of the heat that would be lost down the drain. If your plumbing will accommodate it, it IS cost effective. :dude:
ps: that red plastic pipe is probably PEX which is a good way to go.