Combat leveling (Attack, Strength, Constitution and Defense) is very easy to level the first 15 levels. You don’t really need to pay much attention to gear at this point. But if you want some quick upgrades, you can bank all you stuff. Head over to a high populated PvP world and go across the wilderness wall in Edgeville. Here you can usually find tons of low level (and some valuable high level) equipment that you can use. I usually spend a while here to make some quick gold and get equipment upgrades.
When you are ready to start leveling you have 2 easy options available to you. Men or Cows! Level to level 15 in all combat skills on these, will go quick and you can go over 15 if you want as well.
Option 1 : Men in Edgeville
The first option is killing Men in the house in Edgeville near the wilderness wall. If this area is camped, hop to another world. The Men are level 6 and quite easy to kill, you will probably find yourself one shotting these a lot. They also respawn quickly so you will have 15 in all combat skills in no time.
Option 2 : Cows
Cows can be found many places in the game but my favorite spot is the fields just to the east of Lumbridge. These are also level 6 and is very easy to kill. Most of these you will oneshot and leveling to 15 in all the combat skills will go quick.