My Fire Kit:

REI Storm Matches
Weather/Water Proof Matches
Match Striker (ie emery paper strip)
Coughlans Tinder Cubes
Magnesium Flint Striker
Sparklite
Tinder Stick(s)

Covers emergencies. If you need supplies to start camp and cook fires on a regular basis, add additional quantities.

The magnesium and sparklite are more for emergency use than just firestarting materials.

Note, I also carry a lighter as EDC.