BJT Bias Design and Operating
We are not here to do your homework for you, so I'll just give a broad approach.  Ask specific questions if you get stuck on any individual point.

Decide the gain you want.  I wouldn't try to make a single stage produce more than 10x voltage gain for most normal applications.

The gain dictates the ratio of R1 / R4.

Decide the max current you can afford to have this draw.

At the lowest output, figure you want to keep 1/2 volt on the transistor.  That means the max current from step 3 will be (Vcc - 1/2 V) / (R1 + R4).  That gives you absolute values for R1 and R4.

Find the collector voltage at the maximum current operating point from the previous step.  That will be your lowest output voltage.  This highest will be Vcc when there is no current thru the transistor.  Try to bias the transistor so that the collector volatage will be close 1/2 way between these two extremes.

Determine the voltage to hold the base at to achieve the collector bias point.

Find the worst and best case base currents for the bias point, using the min/max assumptions about the transistor's gain.

Design the R2-R3 voltage divider to produce that voltage using a mid value for base current.  Check what happens at the base current extremes.  If the collector voltage varies too much, then your circuit is too dependent on the transistor gain and you need to adjust something or relax some specs.



Show the values you picked.  For extra credit, tell us the resulting input and output impedance of the amplifier.