Ginger beer is one of those recipes where there are like a zillion variations - and that's just in Trinidad. From what I hear, other islands add pineapple or other fruit to the brew blend. Ginger beer that you get in a bottle in a store is very different to the home made version.
Also, it's not alcoholic - or at least it's no supposed to be. I wasn't sure if that was obvious or not.
My dad always hated ginger beer with too much "stuff" in it. He preferred the ginger to be the star and not things like lime, or a bunch of other spices. He would make it super strong so that it wouldn't take up too much room in the fridge and it would last longer. Just dilute with plain water (or your fizzy water of choice) to taste. In the summer, he'd drink tons of it so it worked out well in our house.
If you have a soda stream, it may work out well as a fizzing option.
Another thing that varies is the brewing method. I've heard of having it sit in the sun for an hour to putting a potato in the mix and having it brew for several days.
The only consistency I've seen is that you always peel and grate the ginger - never chop it up and there's always sugar and at least two cloves in it.