Hi What is the best micro controller i can buy to input a digital high signal to a circuit and receive the corresponding output from the circuit and transmit the response through bluetooth device.
Any of the arduinos will work fine for this. It comes down to size and cost and power consumption. We don't know enough to provide a recommendation, especially for the "best" one.
The smaller the controller better it is and the cost will not be a problem. It would be preferable if it is powered by a 9 volt supply.
Or the 3.3V version to save more power/size as the BT module is 3.3V so no need of voltage level conversion.