Single Stage Transistor Amplifier
At first, you should know that for a common emitter stage the simple gain expression Rc/Re is a rough approximation only. More than that (because you mention a capacitor Ce across Re), this expression does NOT apply if Re is bypassed with Ce (for frequencies higher than the corresponding cut-off frequency). 

Secondly, it is common practice to bias the base with a well-dimensioned voltage divider. Suitable resistor values are derived from a trade-off: The resistive level should (a) as low as possible in order to produce a "stiff" DC voltage (relatively independent on the DC base current Ib and its large tolerances) and (b) not too low because of power consumption and a sufficiently high signal input resistance.

For this reason, it is common practice to allow a DC current through this resistive divider which is approximately I=nIb with n=(6...10).