I carry a small tin box (3'' x 5'' x 1'') from a craft store as my fire kit. In it I have windproof/waterproof matches, a windproof/waterproof butane lighter, a few sticks of Fatwood, a tiny Nalgene container with Vaseline soaked 100% cotton balls, and a few Wet Fire Packs. There is also a few waxed cardboard strips, a ferro rod and custom made striker. Wrapped around the outside of the tin box I have some cut strips of a bike tire tube so they look like rubber bands (they produce a darker smoke if needed.)
Now, knowing that I have all that to use, I would not just yet resort to anything in the tin. I would want to keep it available for as long as possible in case I needed something very quick to light a fire.
l would first build a slight windbreak where I wanted my fire using dry rocks or larger logs. Then on to gathering plenty of dry materials to keep it going (assuming its not raining in this scenario.) I would then utilize primitive skills to start the fire and this would not only help me stay warm until the fire gets going, but it keeps me in tune with skills I never want to lose, not to mention improve on. I would rig a cover over the fire to prevent it from going out in bad weather, and this would help keep hot coals safely contained while I would search for other needs (more wood, water, food, animal runs, etc.)
Having the items for starting a fire does not mean they would be the first things I would use. There is the flint from rocks, fire plow, bow and drill, eyeglass lenses, etc. to use first, so as not to dwindle the emergency quick start items in my tin box.
One other thing many let slip their minds is the lint in the pocket and your own hair to start a fire. Even shaving a sliver of material from a garment hem can do the trick on igniting the flame if all other materials are wet.
I would secure the fire I started and if I had to move on, I would take a little bit of the fire with me. Some hot coals or embers in the tin box I kept everything else in. I would just dump all the tin box contents into my pocket temporarily so I could use the box. I just don't like the idea of using the actual gear I carry unless there is absolutely no other means. I like the idea of always having a backup for everything.