The answer to your second question is using batteries. These store energy but have the disadvantage that they provide a DC voltage - and at relatively modest voltage levels per unit battery (say 12V, as from a standard lead-acid battery).
It really depends on what you are trying to do with this wind generator. One wonders if it is merely experimental, or whether you are hoping to save money. Unfortunately a domestic size of generator only produces about 500W of power when the wind is blowing at a reasonable rate. A DIY perhaps might produce rather less.
It would be possible to rectify the output from an AC supply and store it in banks of batteries - normally done with banks of batteries in series so producing 12V output. But then if you want to use this stored energy back into your domestic lighting circuits, you need an inverter to turn 12V DC back to 240V AC, using a qualified electrician to do it for you. Developments are being made all the time on battery technology - particularly for use in motive power for auto technology.