Are you looking to make a ginger ale with a noticeable amount of alcohol or a soft drink? If you're doing a higher ABV ginger ale, you would follow the same procedure and equipment used in beer making. The only difference for your ginger ale would be the ingredient list (although from therecipeyou posted, it would technically be a ginger mead). The local homebrew shops would be of great help for advice, and a good resource for equipment. Please do not discount them as a source of equipment just because their focus is on making beer and wine, the process is similar.
If making a soft drink, you simply skip the primary fermentation step. The only equipment you need is a heat source, pot large enough to hold the volume you wish to produce, and a sealed container to bottle it in afterwards. The sealed bottle choice is up to you, for inspiration just look at what your favorite carbonated beverages are stored in. the fermentation step is used historically to carbonate your blend after bottling, which will also add a slight yeasty -and sometimes fermented flavor. You have a few options for carbonating if you do not care for the yeast flavor or encounter difficulty achieving the desired carbonation level, some of which are discussed in MC. (http://www.fizzgiz.com/orhttp://www.sodastreamusa.com/) I have used both of those, and they perform well for smaller volumes. If you want to do a few gallons, I force carbonate in aCorneliuskeg with a CO2 tank and regulator, all of which would be available at or through your local homebrew store. Your 'brew' can be served, stored, or bottled straight from the keg.
As far as recipies, i would recommend starting here for ideas:Ginger Ale Recipes
A good introductory book to home brewing relevant to your interest is Homemade Root Beer, Soda & Pop
this is a great one once you have some experience, unfortunately not presented in percentage:
(printed in multiple publications including "Brew Your Own") by Andrew Schloss
GINGER GINGER ALE
The combination of fresh and dried ginger gives this ginger ale an extra layer of flavor, a potent floral aroma, and minimal heat. Because the flavor develops during fermentation, this soda must be made with yeast. This recipe does not begin with a flavor base. Follow the complete brewing instructions to make one gallon of Ginger Ginger Ale.
To Brew:
3 1/2quarts water
3ounces fresh gingerroot, coarsely grated
1(1-inch) length dried ginger
1pound sugar
1tablespoon apple cider vinegar
1/8teaspoon champagne yeast (Saccharomyces bayanus)
1. Combine the water, fresh ginger and dried ginger in a large saucepan. Bring to a simmer over medium heat, stirring occasionally. Let simmer, uncovered, for 15 minutes. Then add the sugar and vinegar, stirring until the sugar dissolves.
2. Remove from the heat and let cool until the mixture reaches warm room temperature, from 75 to 80°F. Strain out the ginger. Add the yeast, stirring until it is completely dissolved.
3. Pour the mixture into sanitized plastic bottles using a sanitized kitchen funnel, leaving 1 1/4 inches of air space at the top of each bottle. Seal the bottles. Store for 3 to 5 days at room temperature. When the bottles feel rock hard, the soda is fully carbonated.
4. Refrigerate for at least 1 week before serving; drink within 3 weeks to avoid overcarbonation. Makes 1 gallon.
