Two stage Amplifier CC-CE with high voltage gain
I really don't want to put up the 'full solution' as I think the OP will benefit from working through the design themselves.

A two stage amplifier is simply a combination of two single stages. In this case a common collector (CC) followed by a common emitter (CE)



This is the generic circuit. The output of the first stage is connected to the input of the second stage.

Task 1 is to work out what values are required in the CC stage to give a 1M0 input impedance.

Task 2 is to work out what values in the CE stage are required to give a voltage amplification of 300.

You can assume that the BJTs are of the jelly bean variety (common types such as the BC458 etc.) and they have a minimum current gain of 100.

Not asked for in the question BUT the values of the capacitors will control the frequency range of the amplifier. Assume C1 is 0.1uF, C2 is 10uF and C3 is 100uF and C4 is 100uF and for the purposes of any gain calculations their impedances can be ignored (Zc = 0).

There are plenty of sites in the internet that will take you through the design steps.