Recommend a Daily Procedure for Boiling

The water in my area is dirty and no doubt full of pathogens and possibly pollution as well.

I can't justify purchasing a water purification system for this hobby, even the Sawyer, so what I'm planning to do (still haven't been backpacking - though I've done lots of backyard and car camping) is somehow collect water at every crossing (unless my containers are already full), filter it through a cheap charcoal filter (Brita bottle filter), and boil it when I make camp. This of course means I've got to carry enough clean water, per person, for drinking and cooking, to last until the next boiling, and I've got to carry at least the same amount of unboiled water so I can prepare it for the next day and transfer it to my clean containers.

Unless I'm overlooking something? Maybe some tricks to make this lighter and easier?

Perhaps I could always make sure to camp close to a source so I only have to carry drinking water and collect again for cooking and next days beverages, but then what if I don't know what the conditions ahead are like?

How many dirty bottles should I carry, and what sizes. How many clean?

Would you boil once a day, or also stop for lunch and boil then as well?

Step me through your process if you boil, or what you would do if you had to boil.

Silt particles inhibit disinfection. If the water is muddy or cloudy, allow the particles to settle undisturbed for several hours. Alternatively, add a small amount of a clearing agent such as alum (aluminum sulfate). The suggested dosage for alum is 1/5 teaspoon per gallon. Mix vigorously and allow to sit for five minutes, stirring twice. Once the silt has settled, either pour the cleared water into another container or draw directly from the top.

Filter the clear water through a minimum of an absolute 1-micron filter or one labeled as meeting American National Standards Institute (ansi/nsf) International Standard #53 for "Cyst Removal."

Filtration alone is not sufficient to guarantee safe water. Disinfect the filtered water by adding two drops of household bleach or five drops of tincture of iodine per gallon of water. After addition, allow the water to sit for 30 minutes to give the chemical time to kill any organisms. Very cold water should rest even longer. Another option is to follow the manufacturer's instructions for commercially prepared products.

OR

Bring the cleared water to a roiling boil for one full minute. At elevations above 6500 feet (2000 meters), such as on the canyon rims, increase the boiling time to three minutes.

Treated water must be stored in clean and sanitized containers.

What kind of pollution? If mining runoff or agricultural chemicals, you might not be able to achieve safe drinking water. "Regular" dirt isn't a threat, per se, but harbors bacteria and makes water unpalatable, so you still want to get rid of it.

How well do Brita filters remove the suspended dirt? They will help with taste and odor, but you might want something else, or in addition, to take out the dirt and not clog the Brita filters.

Are you boiling on a stove or over a campfire? Stove means lots and lots of fuel, while campfires double your work gathering fuel, tending the fire, etc.

I try to never dry camp for just this reason, but in desert conditions it's not always possible. And yes, you'll need double water containers for the dirty/clean sides and that means double the weight at 8.3 pounds/gallon.

My rule of thumb is 1 gallon per person/day, more in hot and dry conditions. Plus, this water has to cool off at some point before drinking.

Honestly, I'd rethink the whole thing and devise a system to remove debris through settling or filtering, then chemically treat. As a starting point, here's what the NPS recommends for the Grand Canyon.