Biasing of CE amplifier with emitter resistor for specific gain
[For best design, add a 2nd Re in series with first R, with no bypassing. These 2 Rs allow stabile biasing and stable Gain.
And thanks to LvW for error detection and system thinking.
Input Resistance will be parallel combination of R1, R2, and the transistor Rin.
The transistor Rin, assuming excellent bypassing of Re, will be Beta/gm where gm is the transistor transconductance.
If you have NO emitter bypassing, then Rin is beta * (1/gm + Re).
[note: had been, in error, beta * (1/gm * Re); thank you, LVW]
[by the way, the method I use here took me years to &quot;invent&quot;. There is no magic in biasing Emitter to 1/3 VDD and biasing collector to 2/3 VDD; and setting Rb1 and RB2 to 10X/20X the Re and Rc, just that you can mostly ignore the beta and the beta variations. In starting out, I used the single_resistor from base_to_VDD as do most newbies; then I learned about Re stabilization for Ie and for gain. I think the GE Transistor manual I was given did show Re stabilization, but I had to slowly learn all the tradeoffs. And even later I still had to learn/visualize the energy sucking o C_Miller_Effect.]
Your instructor is letting you immerse, and learn quickly. Hang in there.
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For a gain of 50X, using a single transistor, with resistive load, first let us be sure we can achieve that 50X.
The maximum gain a single bipolar can provide, with resistive load, is

VDD/ 0.026 volts.

Since 12/0.026 is about 480, then yes, we can move ahead.
Bias the transistor emitter to VDD/3. Bias the collector to 2/3 VDD.
This is very stable biasing.
You have no required Vout_peakPeak, despite that Rload.
Bias the transistor to 10mA (why not? power is free).
The transconductance &quot;gm&quot; is Ie/0.026 volts = 0.010  / 0.026 = 1/2.6 ohms.
The gm is 1/2.6 ohms. For a gain of 50, set Rc = 50 * 2.6 ohms, or 130 ohms.
With 130 ohms as Rcollector, we will mostly ignore the Rload value in computing the Voltage Gain.
Set the Re to 130 ohms also. Pick a very large Ce, to ensure Zc &lt;&lt; 2.6 ohms.
Make top base bias be 20 * 130 ohms
Make bottom base bias be 10 * 130 ohms.
Done.
For high bandwidth, you might worry about C_Miller_Effect.
At high frequencies, that charge consumption will suck up lots of input energy.
I ignored any source impedance.
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If you must have a high Rin, then consider a Darlington. Which also gives you some flexibility about handling C_miller_effect.