This may not be the *easiest*, but I find it very easy. 1. Kill chickens of rats until you get to say, level five 2. Then go behind Lumbridge Castle, and kill the giant rats (level 3). 3. When you're a level 8, go kill the Mugger behind the castle (level 6), an added bonus, you can get rope or coins. 4. You'll get more experiance if you fight people who are closer to your skill, but I say, have a, 3 point advantage. just in case.
Alternate between block, stab and slash, your total combat will go up faster.
Keep lots of food handy! - xmimix 666