I have done the recirc both into the bottom of the water heater, removing the existing drain and installing a tee for the recirc,
And I have used the incoming cold for the recirc. Normally for the incoming cold, I would have a check valve to prevent the recirc from going upstream, and add an expansion tank.
Regardless, I use a spring check on the recirc line.
The Aqua Stat is a nice touch on the recirc. It shuts the pump off when the heated water has completeted the loop.