Soda is the supreme elixir of life, and it does not need to be "brewed". Why not start out simply, and only introduce complexity as some need becomes apparent.
One simple approach is just to crack open a sealed plastic jug of juice (room temp cranberry works well) and chuck a bit of bread yeast into it and recap, squeezing out most of the air. Drawback is, you need to be there whenever IT decides it is ready and is bulging with bubbles several hours later. Oh, you can fridge it after it gets going to slow it down a bit.
Next step in complexity is a sodastream machine... comes with co2 bottles and their own flavors, which I hate. Anyway try another brand root beer extract plus syrup, or just simply frozen juice concentrate, like lemonade... yum.
If you like the result or potential, I hope you bought one of their models with a thick base which can contain a paintball container. Get one of the many adaptors online to a 20oz or so paintball flask and cut your co2 costs to near nothing. You may also wish to buy several of their empty half liter bottles so you can stock your fridge with a variety of prepared sodas.
I have written various threads that try to refine the above approaches. Failing that you can scroll the pages here for various heavy metal approaches...