I've used the Britta Activated Charcoal Filters made for the "Britta Squeeze" bottle for several years now. They work very good.

I'm doing exactly what you describe, the only difference being the source of water. We have lots of good clear water here, but we also have feral hogs and other critters than do contaminate it in some areas, so filtering plus boiling is a fine option.

I use collapsible water bottles. Enfamil, the baby formula company, makes some, and there are others out there. All of them I've found accept the Britta filter perfectly.

My advice is to camp near water when you can. If that's not an option bring extra collapsible bottles and fill them as opportunities present themselves. They don't weigh much and they pack down to hardly larger than the size of the bottle cap.

I quit using expensive filters about 4 years ago. There's really not a lot of advantages over the method you're wanting to use, and my own experience it that it is a lot more reliable.

The only thing I'll offer is don't squeeze the water through the filter as fast as you can, be gentle. The longer the water is exposed to the charcoal the better it filters it.