Difficulty with Common Emitter Amplifier
I think a single transistor solution won't be good enough - you have to consider the standing DC currents when no microphone is present - these will likely still illuminate your LED and this is not what you want. Here's a circuit I designed many, many years ago and I've added a third transistor stage on to drive a LED: -



You might find it's a little too sensitive for your microphone but that can be reduced by increasing R3. It's output stage is designed to drive a 20mA LED hence the 390R resistor for R5. With no sound present the LED will be off.

The circuit; Q1 amplifies the input signal and Q2 rectifies the level converting AC signals into a DC level on its emitter. It's self-biasing and draws only a few micro amps when the mic is inactive. C2 smooths the rectified signal on Q2's emitter and this feeds Q3 which gives the signal enough grunt to drive the LED.