How to be a pure Ranger.

First step:
Making your character.
Make your character and give it a cool name.  Finish tutorial island with all stats 1 if possible.  Make sure that your Attack, Strength, and Defense are 1.

Second  step:
Gathering supplies.
Run to the goblin house (across the bridge from lumbridge) and gather as many bones as your inventory can hold.  Run to the grand exchange after that and sell all of your bones at minimum price.  If the price stays the same as now then that will give you 2.8k.  Next run to Lowes shop (its in varrok) and get 30 free bronze arrows and 1 free shortbow.  Now we are going to spend you 2.8k.  Run back to grand exchange and purchase a leather body, cowl, leather chaps, a power amy, (You may need to save up some money for this) a leather vambrace, some leather boots, and any colored cape.

Third step:
Range level 1~10
Run back to lumbridge and on the way you should see a chicken coop.  Start ranging those until you have 5 range. (make sure you collect the bones and feathers)  At 5 range you can wield Oak bow.  Run back to lowes or grand exchange and purchase a oak shortbow.  You can also purchase some iron arrows to hit harder if you have enough money.  Go back to chickens and continue training here till 10 range.  
Range level 11~20
Now you are ready for cows.  I use the place near lumbridge on the way to varrok but it is sometimes crowded.  After a kill make sure you grab the cowhide as that will make money for the arrows.  Range here till level 20.  Go to lowes or Grand exchange again to buy willow shortbow.  Also you can now buy studded leather chaps, and a coif.
Range level 21~30
Here you have a choice.  You can either go to barbarians or you can start ranging guards.  I chose barbarians because the guards require food.  Anyhow range here till 30 range.  The gaurds drop grapes that you can take.  And the barbarians have the rare uncuts.  Both have bones.  At 30 range purchase a maple shortbow.  Congratulations! Now you have the best bow non mems can have.
Range level 31~40
From here on out you can range minotaurs because they drop iron arrows.  Another option would be to continue ranging barbarians or guards.  The minotaurs are located in the stronghold of security  in the hole in the middle of the barbarian village.  Once you have 40 range you can now wear  Green d'hide armour!!  The best range armour for non mems!  This is the final set of  equipment you need.  There will be nothing else you need to buy.
Head: coif.
Body: leather body.
Amy: power amy.
Legs: Green d'hide chaps.
Hands: Green d'hide vambraces.
Feet: Leather boots.
Arrows: Any kind you want.
Cape: Any colored cape.
Range level 41~80
My recommendation would be moss giants as they drop big bones.  There are many other choices but the moss giants would be the best exp.  The moss giants can be located on Crandor.  Make sure as to use safe spots because of your low defence.
Range level 80-99
Lesser demons would be best xp.  If you want to you can go to greater demons or hell hounds but its not recommended.