We were told the water is too cold for efficient heating and then someone else said it would depend on our selecting the "right" tankless water heater. So what s the right one?

Selecting the "right" tankless is the key. You have two different conditions. One is if the system has been off a while & thus cooled off (water now at room temp). The other is maintaining hot enough water during a call for heat. The water going into the air handler needs to be at least 140*. Figuring on a 20-30* drop through the air handler, now you are talking about heating water from 110-120* back to 140 instead of heating 70* water to 140*.