Plenty of good advice out there already but I'll chime in with my 2 cents because I've recently been tweaking my gear for this purpose.
Totally agree with all the filter recommendations. I have a Katadyn Hiker Pro and love it. After drinking that cold mountain water for a week the water back home will be a big disappointment to you. Downside to the filter is bulk and weight. Even if you pump it dry each time you use it, it will retain some water and with that factored in they'll all weigh close to a pound. That said, I wouldn't trade the taste of that filtered mountain water for all the super-small, super-light chemical treatments in the world.
For cooking, if you're only going to boil water for freeze-dried meals or coffee, check out the Halulite Minimalist cookset (~ $25) and pair it up with an iso fuel canister and a Snow Peak Giga Power Stove w/ piezo igniter. The whole works--fuel, stove, spork & pot gripper fits snugly inside the pot. That alone is priceless, but it also comes with a snug-fitting lid, which will shorten your time to boil and conserve fuel, and a neoprene sleeve to slide over everything when you stow it in your pack. All of these stoves will leave a little black soot on your cook pot, so the sleeve will keep everything inside your pack clean. The igniter is a nice to have...just speeds everything up if/when it works, but you'll want a backup lighter of some sort too.
I used an MSR Pocket Rocket on my last outing and it worked great, just won't fit inside the Halulite Minimalist like the Snow Peak will.
If you're really going to be miles out there, consider bringing an Esbit as a backup. You can fit several tabs in it when you fold it up, it weighs virtually nothing, and in a tight spot you can burn twigs in and get the job done.