If using an outdoor water source, I'd be inclined to 1) filter well, 2) boil, and then 3) treat with bleach. Filtering through the layers of cloth/earth/gravel of an expedient filter will remove solid contaminants (including radioactive dust particles) and some dissolved toxins, if I'm not mistaken. Boiling kills microbes, parasites and such. After that, the bleach just makes me feel better.
Fwiw, I'm pretty sure that it's NOT recommended to use a water source that is obviously contaminated with petroleum products or pesticides, which would include most surface water after a flood or other serious disaster. That leaves natural springs and wells, neither of which would be available in many urban settings.