First Co Air handler + Gas Hot Water boiler: Connect thermostat for gas or electric?
I'm going to try to explain this as simply as possible. Most air handling units having several speeds available on the motor usually at least 4. Normally the board will have at least two speeds, one for heat and one for cool. In the old days the lower heat speed was to eliminate the possibility of flue gas condensation as the units, be it oil or gas were not designed to handle the slightly acidic condensate. Nowadays most units are high efficiency condensing units. Everything is still designed around the lower fan speed, and that's a good thing. It's quieter, allows for a longer and thus more efficient heat cycle. All the heat loss calculations, duct sizes, unit capacities and fan speeds are set up with this lower fan speed in mind. Electric resistive elements generate alot of heat for the resistive metal handle and need the higher fan speed to remove the heat before burning themselves up.

Air-Conditioning has a very specific cfm(cubic feet per minute) per ton of cooling. 400 cfm per ton of air across the evaporator. So if you have a 2 ton air-conditioner you need 800cfm.

The thermostat on cooling energizes R(24v) to Y(compressor) and G (fan). On heat with gas selected, as you know energizes R to W(heat).

In your case, running a hydronic coil it's a balance between comfortable noise level, capacity and efficiency. Being connected to a water heater and not a boiler, return temperature is irrelevant. So that rules out efficiency concerns. If it was connected to a boiler then the lowest return temperature possible is ideal. So that leaves comfort vs capacity. At lower fan speeds capacity is diminished. As long as your house is comfortable at the lowest fan speed then that's the way to go.

On modern units there are sometimes dozens of available speeds. By setting dip switches you can select the desired speed in cfm for the application you can even set a baseline continuous fan at say 200 cfm. Then have a separate speed when the board senses power on G(fan switch on the stat set to ON) say 400 cfm. Then for your 2 ton air-conditioner when the board senses power on Y it goes to 800 cfm. Units with this capability are often modulating and the heat speed is set by an algorithm in conjunction with the burner speed. It will start on a very low setting at the start of the heat cycle and ramp up over time or based on indoor temperature readings.

Conclusion


Yes it makes sense
Gas is a good setting
Run the heat as low as possible to maintain a satisfactory level of comfort balanced with noise. And don't touch the air-conditioning speed on the board.