When in doubt, boil and then filter. Or filter and then boil. There are many situations where boiling alone will make the water even less potable than it was before. When you boil you will kill almost everything, but all that is actually removed from the water is some of the low vapor pressure organics. That and some of the water itself. Everything else is now even more concentrated than it was before because some percentage of the water has been boiled off.
Boiling will leave all the metals, most of the organics, all the salts, all the carcasses of micro-organisms, worms, etc. that the boiling killed off.
The safest purification would be to pre filter the water and then hard boil the water, preferably in a pressure cooker if you are at any altitude at all, then distill it at a lower temperature, then run it thru a hefty carbon filter to remove the organics that will sneak thru. Even then you are not left with just water. Of course I am a pessimist. But if the situation is dire, the landscape has been changed and you have one shot of getting "out", one little slip with the drinking water can leave you helpless for days, or worse.