A few comments regarding the original poster's schematic:
The power supply to the op-amp is only 5V, yet the input voltage is also 5V, so even if it has a rail-to-rail input and output, it won't output any more than 5V.
M1 will need to be a logic level MOSFET with a low threshold voltage.
The MOSFET will have some capacitance, causing the gain to tend towards 1+R3/(R1||R2) at higher frequencies, when it's off. This will result in over shoot on the output, as the higher frequencies are amplified more.
What's going on with C1? That'll AC couple the signal, so the output will swing negative, as well as positive.