The answer to a is really only something you can answer. What is it that you find to be important with your system? A basic transfer function has 1 input and 1 output. You can handle more but Im going to assume it is SISO for now. The input you choose will want to be one you can control pretty well.
The easiest way, to me, to find the transfer function is using matlab pidTuner. They, when in the gui choose your plant by selecting to identify a new plant. Most likely you want to look for something called the step response. After you have chosen your input and output signals, start measuring with the input off, then turn it on to some value and wait for an amount of time representative of your system. You can take that input and output data and put it into the system identification to start fiddling around to find a transfer function that fits.
Apparently there is another gui brounght up by systemIdentification but I have never used it.
