\$R_e\$ when using a common collector amplifier
The chosen value for RE depends on the value of RL.
If RE is too big compared to the value of RL then, when Vout swings negative, at some signal amplitude the current through RL will equal the current through RE. This will reduce the current in the transistor's emitter to zero mA and negative clipping of the load voltage will occur.
So you need to ensure that RE is small enough compared to RL (taking into account the maximum required signal amplitude). This may mean some significant emitter current if RL has a fairly low value which will mean a fairly small value for R1 which is required to set the base bias high enough given that the emitter current and therefore the base current are larger as a result of the smaller RE. Unfortunately lowering the value of R1 will reduce the input impedence of the stage with a possible reduction of gain when the output impedence of the preceding stage is taken into account.