You need to do the calculations to figure out the amount of energy that will be produced by the wind turbine over, say, 7 days.
It is also essential to know the extreme maximum power that could be generated (presuming the minimum is 0). It would be a complete waste of time designing for low power and then have the system blow up the first time there is a strong gust of wind.
Without this fundamental information none of the rest of the issues can be dealt with properly - including such things as battery size.
If you have an AC output at a too-low voltage why not just use a transformer to increase the voltage?