yes, water in the separator (gatorade bottle). right out of the tap too. it doesn't get any simpler. i fill pretty high up to just where the plastic starts to curve (gas out tube cut close to the lid). though some co2 gas will be dissolved in the water i'd think it would hit saturation rather quickly and make, for practical purposes, no difference at all.
remember to drill your holes in the lid smaller than the circumference of the tubing you use and yank it through with pliers. unless you NEED the pliers to pull it through it just won't be tight enough to be sealed.
and btw, i use extra tubing from those hagen kits to connect everything. works great. i thought initially that there was no way that tubing that hard could be sealed so thoroughly without some sort of gunk/glue/sealant.
get a glass diffusor when you get tired of dealing with that ladder. i did, after years of faithful use (they do work great), and i'll never use a ladder again. i splurged and got the pollen diffusor from ADA but people around here say the inexpensive ones work just as well (some even use those wooden airstones that you can buy for a dollar).
good luck with everything. you'll be amazed, as i was, as everyone else was the first time they added co2, when you see what a difference it makes.