I'd be inclined to go with an off-the-shelf wind-powered electric generator running an off-the-shelf electric compressor with a big and well-sealed tank.
This way you can switch to mains power and still run the compressor on a calm day.
Doing a direct-drive would be tricky, as you'd have to make sure that both your turbine and your air pump were operating in the correct speed range under all wind conditions. Also, it's going to be a PITA when you want air but can't get it because the wind has died down.
Honestly, I expect that on a homeowner scale this will probe to be less cost-efficient than just running an electric compressor the normal way.