Fast Combat Experience F2P:

Fight monsters in this order to get fast combat experience:
1. chickens (In Lumbridge or betwee Port Sarim and Falador)
2. Cows (Lumbridge or between Port Sarim and Falador)
3. Alkharid Gaurds (At Alkharid Palace)
-  Dwarfs (In dwarf mines near falador)
-  Barbarians (In Barbarian Village)
4. Scorpians (In dwarf caves or Alkharid mine)
5. Outlaws (Left of Grand Exchange near Edgeville)
-  Red Spiders (In Varrock Sewers near Moss Giants) OR (In Lumbridge cave near Lesser Demons)
6. Giant Spiders[LeveL 50] (In the third stage of Barbarian Stronghold) Hint: its green.

This is what I think is the best method because it works for me, this is not garenteed the
best Method, this is my opinion on getting fast combat experience.