Dan can speak for himself about his windmill kits, but of course you seem to have the right impression: the 10-foot windmill should be used at 24V or even 48V. From a simple aerodynamic point of view, the 7-foot diameter sweeps half of the area of the 10-foot diameter, hence it will collect 1/2 the energy for the same wind.
Here's the math: Watts = Volts x Amps
1200 Watts = 12V x 100 Amps
You need very heavy wire to carry 100 Amps without getting very hot or wasting a lot of power with voltage drops, etc. Depending on how long the cables must be, you're looking at US#0 gauge or more.
On the other hand 24V x 50 Amps = 1200W. Wire that can carry 50 Amps is much more manageable; say US#4 gauge.
Look more carefully at the specs of the batteries you want. It's very important to do the same math as above and compare what you put in to what you get out.
Since you house is 120VAC (or maybe you're in europe, you haven't specified) you need an inverter to marry up the battery DC to the house AC. Once you interface one power system to another, you are confronted with the safety, reliability, and building code issues that come along with household wiring.
Nobody said it was easy, but to many of us, that is exactly what's fun about it! :-)
Tell us more about what you want to do, if you like. We're all about getting as many people addicted as possible.