If you google "Yeast Ranching" you'll find some instructions for growing and storing strains of liquid yeast - home beer and winemakers do it quite a bit.
Some hard core yeast ranchers go all the way to plating them on slants like in a lab, and reculturing them from a few cells at a time.
Water and sugar isn't really an ideal food source for yeast, they do better with some other nutrients and minerals as well. If there's a brewing shop around, malt extract can be bought in power or syrup form. Apple juice (without sorbates) can also be effective, but you need to wcth the labels closely. Otherwise it will have so many yeast inhibitors that you'll kill off the yeast.
I'd skip adding the flour from your next steps, and stick with more of a liquid solution. As the yeast multiplies and ferments, it will do two things - first it will foam up at the top of the liquid (high krausen), then drop out of solution and settle to the bottom (called flocculating). If you take it from either state, it will be far more healthy and active than dried yeast, so plan accordingly - especially from high krausen.
Hope this helps!