To design a Neural network for binary classification, We use a single neuron How to know which output function to apply in that neuron? i.e. Linear threshold or Sigmoid?
'Output' function? You mean activation function! It depends on your specific case. And why do you want to change it in the first place? Stick with Sigmoid until you figure out you need something else!
PS: why are you only interested in changing the activation function of the output neurons? (vs. hidden neurons as well)