My "Young Instruments" helicoid propvane (which is a proper WMO spec instrument) produces a small AC output, the frequench of which is proportional to windspeed.
Rather than converting freq to voltage, then reading with an ADC (both of which intruduce errors), consider measuring frequency directly.
My old original weather station (circa 1985) was made without reference to any existing design. I took the AC from the head, through an op-amp set with basically open loop, and the two AC leads to + and - inputs. The resulting (nearly) squarewave output was fed to a 12-bit counter.
Under software control, I would read and reset the counter and store a times (in milliseconds). This gave me a count, and a time over which it happened, that directly converted to frequency with virtually no error (just timing error, which was minimal).
Using todays PIC and microcontroller chips it'd be even easier as they have all that built into them.