Looking to make something really tasty, and also non-alcoholic. Is this possible to achieve at home?
There are two ways to do this:
To make "real" ginger ale, you actually ferment it using an appropriate recipe and either a baking yeast or an ale yeast. This gives it the carbonation and the proper flavor. Very tasty, slightly tricky, but unavoidable to make it very mildly alcoholic.
To make what's sold in stores as ginger ale (which is completely non-alcoholic), you actually make a ginger syrup, then carbonate it with soda water.
There are plenty of recipes on google for either technique. Personally I prefer making a real homebrew ginger ale, and with the right yeast and a lower amount of initial sugar you can keep it very low on the alcohol content.
Basic, carbonated beverages made using yeast will technically have a bit of alcohol, but VERY little when compared to beer, much less wine or hard liquor.
Whenever yeast is in a liquid that has sugar in it, it consumes the sugar and leaves behind some alcohol and a lot of carbon dioxide bubbles.
For beer and wine brewing, the carbon dioxide is vented off for most of the process, leaving the alcohol behind in a relatively "still" liquid.
After that, if you want carbonation, when the yeast has eaten all of the sugar in the liquid, a tiny bit more sugar is added and the beer and the whole thing either bottled up or put into a sealed keg. That sealed container will then force the carbon dioxide that the yeast produce while eating that "priming sugar" right into the beer, giving you the carbonation.
For soda, you can effectively skip the step where you turn all of the sugar into alcohol and just do the bit that turns a tiny bit of the sugar into bubbles. This does result in a tiny amount of alcohol, but so does making bread :).
Mix up your base sugary liquid, which in this case, I'd go with grated ginger, some lemon juice and something like a cup of sugar per 2 liters or quarts.
Pour that into, for example, a 2 liter soda bottle and add a packet of yeast.
Seal the lid and set in a room temperature area or slightly warmer. I tend to put this kind of setup on top of my refrigerator.
For a couple of days, check in on it by seeing how firm the bottle gets. It should start out with some "give" and start getting so it's less easy to squeeze it. When the bottle is no longer "squeezable", put it into the refrigerator for another couple of days. This will stop the yeast from consuming any more sugar and let them die off and drift to the bottom of the bottle along with your grated ginger.
From there, you can drink it like you would any other soda. This approach works with pretty much any high-sugar beverage you want, as long as it doesn't have preservatives in it. Preservatives will prevent the yeast from doing their thing. It can also work with "diet" beverages too. Just sweeten with stevia or similar and then put in a couple of teaspoons of sugar per gallon. The yeast will use the sugar and your final beverage will have very few calories.
You can do the forced carbonation version instead at home with household ingredients too, though the carbonation achieved this way is less "deep". Beverages with brewed-in carbonation have MANY more tiny little bubbles than you can easily get with forced carbonation. That's because the carbon dioxide is more dissolved in the brewed liquid.
Anyway, to force carbonate at home, take 2, 2 liter soda bottles and drill holes in the caps. Put a bit of tubing into those holes to connect the 2 bottles, making sure the tubing fits without a gap (I sealed mine on the outside with silicone sealant).
In the one bottle, put your beverage. In the other, put a cup of vinegar.
Take a few tablespoons of baking soda, drop it into the vinegar and quickly seal up both bottles. The baking soda/vinegar reaction produces carbon dioxide much more quickly than yeast and sugar does and will force that CO2 along the tube into the other bottle.
Let it sit for a bit and then replace the "tube cap" on the beverage bottle with a normal cap and put the beverage in the refrigerator to enjoy.
Here's Alton Brown's recipe.
The yeast will produce minute amounts of alcohol, but it's nothing to worry about. I would let any kid drink this.
If you're really worried about it, just mix the syrup with some club soda.