I have an Air-X made by Southwest Windpower on the roof of my cabin. It has been up there about 4 years and has performed the way I expected it to--that is, as an auxiliary source of power during short, stormy winter days when the photovoltaic system is not producing much. It's rated at 400 watts @28mph, which doesn't mean much by itself, except to say that it's one of the smallest windmills available. The windmill is mounted on a pole attached to the end of the cabin, extending to 27' above ground level. the windmill vibration is dampened with old automotive motor mounts on the roof where the pole connects to the end of the peak. There are also 2 pipe struts extending diagonally out to the eaves to stabilize the tower. These are also dampened with motor mounts. The Air-X costs around $600 but includes a controller, which you'll need anyway to regulate the power to your batteries (which you'll also need, btw, to store power). If your toolshed has 120volt AC appliances, you'll also need an inverter, unless you put 12 volt lighting in the shed instead.
If you were to mount the windmill on your toolshed you might be able to get away with a bit more height than 14', as long as the neighbors don't complain about the noise. In big winds, the Air-X can make some pretty amazing noises, as it gets turned away from the wind by a vortex. Unless you live in an extraordinarily windy area like I do out here in the desert, it probably won't give you much power. One advantage to a windmill however, is that during storms it can produce day and night, which can add up over time. With the batteries, wires and pipe, you'll end up spending at least $1,000. Patience is right---photovoltaics might be a better project in this case, but not less expensive.
Southwest Windpower Air-X
"Wilderness is another civilization apart from our own." - H.D. Thoreau