Should I pursue building my own wind turbine?
A generator would probably be a better choice. 

You haven't given us a lot of details, so I'm going to assume that you live in norther US,  Canada, or the UK, that you live in a middle-class detached house with a yard, and that you're faced with winter storms taking out your power for a day or two, and you want to keep the fridge cold and run a few lights until the power comes back on. You will burn something (propane, kerosene, wood) to stay warm, cook food, and make tea.

The main problem with wind power is that it's not necessarily available when you want it. During a storm it may be so windy that the turbine shuts down to protect itself. After the storm there may be 0 wind. You'd need a way to store electricity, which means banks of deep-cycle batteries, a charge controller, an inverter. As long as you have the batteries and electronics, you can charge off main power when that's available, and don't need the turbine as much. Batteries are expensive, they go bad after 5-10 years, require good care. 

A generator provides you with power exactly when you need it. You can store an enormous amount of energy on site in a tank of diesel of gasoline, and you can buy more with a trip to a gas station, for long outages. If you already have propane or natural gas on site, you can get a generator that uses that fuel, which is way less hassle than pouring fuel in to a tank in bad weather.

If your loads a small and your expected power outages are long, it might make sense to get a small battery bank + charger + inverter to accompany your generator. Turn on the generator for a couple hours in the evening, so you can check your email and run some lights and charge the batteries, and draw on the batteries for the small loads the rest of the time.

So, it goes like this:


Identify and minimize loads
Install a generator with transfer switch
Upgrade with a battery bank, charger, and inverter, if needs dictate
Upgrade further with wind or solar power, per budget and interest