It would be ok to build the pulse generator and the buffer chip on a bread board, but due to the high current pulses, not the inductor, Mosfet, and output diode. Also note that the circuit only use half of the 4049, do not leave the unused inputs unconnected or strange things can happen. All inputs must go somewhere, best to connect them to the negative of the supply. you can leave the unused outputs floating.yes, nice. can i build it on standard breadboard?
most any N channel power mosfet works in that circuit as long as it is rated at 200 volts/15 amps or greater. Mount it on a suitable heatsink.
When you don't have a load connected, depending on the inductor you use, you can have very high voltage spikes across the Mosfet.
I found that the inductor is also not critical, anything from 200 to 400 micro Henries will work ok, but it needs to have a reasonably large core and thick enough wire (24swg minimum) to handle the current of the pulses which can be up to 40 amps. Look at the picture of the one he used.
All the ones I had success with were reclaimed from scrap plasma tv power supplies as were the Mosfets and shottky diodes.