what sampling rate and bit depth should i use?
The typical audio sampling rate is 44 kHz, so you would need between 130 000 and 175 000 samples.
In practice though, it depends on the sampling rate you use on your FPGA. You can lower, but you will need to low-pass your signal before sampling it to avoid aliasing.

Note that if you put a threshold on z[n]=x[n]*y[n], it will not be invariant to volume differences.