This is what I do for my brew days (or the night before if the brew day starts early)
Guesstimate how much water you'll need. If yuo have a 5 gallon extract batch you'll need at least 6 gallons of water maybe more depending on how strong your boil is. So what I do is take any container that won't be used for brewing (another kettle, growlers, pitchers etc.) and fill them up with that much water as you need, or if you come a little short can. I filter all mine using just a plain old brita filter. WOn't get rid of all of the contaminants but enough for my liking. After you've filled up your kettle and started a boil/mash you have an hour of down time, so then you just go and filter off some more water and keep some reserved. It's water, it's like 2 tenths of a cent per gallon, and you can drink it, so if you have too much prepared, drink it later.