Input and Output Resistance of an Amplifier
But I have no idea where to start finding Rout


Look at the standard graph of a BJT's characteristic: -



Choose a base current - say 60 uA

Look at the change in collector current (\$I_C\$) versus the change in \$V_{CE}\$: -


change in \$I_C\$ is about 0.25 mA
change in \$V_{CE}\$ is about 5 volts


The slope has a dynamic resistance of 5 volts / 0.25 mA = 20 kohm.

This is the effective "raw" output impedance of a BJT operated in common emitter. That raw impedance is in parallel with R1 as far as AC signals are concerned hence, if R1 is significantly smaller than the innate collector impedance, then a decent approximation to the circuit's output impedance is R1.

At higher frequencies than a few kHz, we also take account of the miller capacitance (internal capacitance between collector and base).