I put the ginger in the new batch along with the mother and it will stay there for the next 10 days until I strain it out.
We tried the most popular brand of Kombucha drink that is marketed: GT's Orgainic Raw Kombucha. We tried the Cranberry and Gingerade. The cranberry tasted like pure vinegar, the gingerade was really good.
GT's kombucha is bottled with the live bacteria and from what we'ver read, you can actually buy a bottle of GT's Kombucha drink, and use it as a Kombucha starter, and it will grow a mother. It may take a few batches before you get a good mother, and a drinkable batch of Kombucha, but it's supposed to work. We bought ours at Sunflower Market here in Albuquerque, NM. You should be able to find GT's Kombucha at Wild Oats, or the equivalent. It's about $3 for a bottle, which is very high for a drink, but if you're going to use it as a mother, it's not bad.
I haven't heard of using other juices to make Kombucha, but I'm new to this myself.
I use juices to make KEFIR, which is very good!