Forget the paper, commercial fire starters, cook stove gas, even the birch bark that may not be around anyway. Get yourself an old bicycle inner tube (the skinny kind from those real narrow tires), cut it up into 2 inch pieces, and put them in a ziplock bag. Even on soggy, rainy days, put a match or lighter to a piece and get a good stubborn flame that will burn for several minutes, long enough to get even damp twigs and tinder going. The cylindrical shape is the key, so don’t slice them lengthwise to save room in your pack.
To be on the safe side, however, I also carry a back-up fire starter in my gear bag. It is never much fun--and possibly life-threatening--to be caught outdoors in foul weather without the ability to get a fire going. I bring several cigarette lighters, plus several different waterproof containers with strike-anywhere wooden matches--plus a dry piece of sandcloth to strike them on, in case there is nothing dry available for a strike surface. I use a short piece of plumber's sandcloth (for cleaning copper pipes before soldering), rolled up and stuck in with the matches.
And, of course, birch bark is a wonderful thing, but only available in certain regions. I have rarely had to move past one piece of bike tube to start the hundreds of campfires I've enjoyed over the years. There's just nothing like a good campfire!