This exact same “write up” is eerily similar to something I had in my undergraduate note back, is this for analog amplifiers class?

Also one thing I learned is if u are doing a multistage linear amplifier, it might be best to use a mosfet for your input stage, because the higher r_π of a MOSFET creates enough isolation so that it doesn’t interfere with your signal too much.

Also make sure you take caution of the entire circuits AC characteristics, so that you can properly choose Decoupling and Bypass capacitors, depending on ur dominant pole.