Funny, I just brewed my ginger "beer" today. I keep it on tap and it goes quick. I've played around with hopping it, and adding other ingredients, but the core is..
10Gal batch
1.5# real ginger, sliced thin
~20lb sugar, I use turbinado style for some color and molasses taste
8 lemons
8 limes
Sometimes I will add a bit of powdered ginger(up to one of the larger plastic cylinder containers 8oz?)
yeast nutrients per instructions
~12.5Gal water
I boil the water, and as it comes to a boil I add the ginger
boil 1 hour adding the nutrients with ~15 minutes left
I have added the sugar with 15 mins left, and chilled at the end, though the last few batches, I put the sugar, lemons and limes into the fermenter, and added the "tea" at boiling for a no-chill method.
Make sure the sugar is dissolved either way, and add thinly sliced lemons and limes to the fermenter.
Pitch yeast at pitching temp.. I've had great luck with champagne yeast, S04, S05, voss kviek, the current one, brewed today is going in with Belle Saison and fermenting slightly warm to see how it comes out.
I tend to get something along the lines of a Reed's ginger beer, but at 8-9%abv
I also keg and keep the pressure up a little higher, so I get closer to a soda, and fementation happens in either a 15Gal conical or a 15Gal keg with a 4" triclamp port. I'm sure you could scale, and probably bottle though I would use sturdier bottles if carbonating higher than a standard beer, and I would suggest only doing no-chill in a stainless steel container as it could melt plastic, and I don't even want to think about glass.
Anyway, Thanks for listening to me ramble.. This stuff typically goes quick in my house, but my newly 21 son did it with me today, and I think that might become one of his chores..