Adding expansion tank with flow control to newly replaced water heater

[goofy78270]

I recently replaced my water heater, but when getting it inspected, I was told that I need to add an expansion tank. I also noticed that after sitting for a while, the cold inlet line tends to get warm due to the back pressure.

I have looked through the 2018 code, which my current jurisdiction used, but am unable to find an answer to my question.
With the addition of the expansion tank, can I also add a flow control valve to the cold inlet line to force all expansion into the tank rather than back fed into cold line as well? If so, should the control value go before or after the shutoff? Also, I have seen the expansion tank installed before and after the shutoff...does location really matter?

Side question, what are thoughts on an TXV, thermal control value, versus an expansion tank?

 

[RS]

I have always been on a well and have a pressure tank, and have never needed an expansion tank. When the water in the heater expands it just pushes some water back into the pressure tank, but it's normally a very small amount. If we were to use all 50 gallons of hot water quickly, I would imagine then it would be noticeable, but we never do that. It's possible in the near future we are going to be hooking up to city water, and if we need a PRV with a check valve then we may need an expansion tank.