Preparations
The items you'll need to become a strength pure are iron full helm, iron plate body(or chain body), iron plate legs(or plate skirt if you are a girl), an anti dragon breath shield, green d-hide chaps, green d-hide vambrace, all the scimitars from iron to rune, a short bow, 6000 arrows, strength amulet, and lots of food.
If you want to train your mage to teleport you will also need an air staff and lots of mind runes. You can forget about the black scimitar because it is rare and expensive it cost me 10k for a black scimitar. All these items should cost about 100k. (Including the black scimitar.) In the picture below, all the things you will need are in my inventory. (Note: You will need a lot more food then what's in my inventory.
Start to Train
First off, wear your full iron set, the anti dragon breath shield, and an iron scimitar, a strength amulet, and a cape if you want. Leave a steel scimitar in you inventory and put the rest of the things in your bank. Go to the chicken farm across from the cows and just east of Lumbridge.
First train your attack to 5. Once you're done that, wear your steel scimitar, and train you strength to 10. Now that you're done training strength to 10, you can move on to the cows just across the road, and train your attack to 10. Then you have to train you strength to 20. You could bring food if you think you'll need it.
Next get your black scimitar and wield it. If you don't have a black scimitar, then just use you steel scimitar. Head over to Al Karhid, and train with the warriors. Be careful because once you attack one of them, another warrior will come and fight you!
If this feels too hard then you should train with the cows. Train you attack to 20. Once you're done that, train your strength to 30. Now that you're done that you can keep on training here, or go somewhere else that's stronger. I recommend staying here because these guys are pretty strong. Get out your mith scimitar and train you attack to level 30, and your strength to level 40.
After getting your strength to level 40, wear your addy scimitar and get your attack to level 40, so you can wear the rune scimitar. You should be able to hit 8 or 9. If you can hit 10 or higher, you're doing better than me.
Go Pking If You Want
You are allowed to go PKing (player killing) now if you want, or you can still train.
Back to Training
You can still train your strength to 70 here, or you can go to the Hobgoblins south of Port Sarim. These guys are pretty strong. You should bring salmon to tuna as your food. Train your strength to level 70 here.
Time for Ranging
The reason we're ranging is because when you are PKing, you will be able to kill rangers easily, but you will mostly die from magers. We want protection from magers. That's why we wear the anti dragon breath shield, but we will need more protection. This is where the green d- hide chaps and vambraces come in.
Green d-hide armor give good protection against mages and also has better melee defense than iron armor! We don't want to wear the green d-hide body because that requires 40 defense. To wear the green d-hide armor, you need 40 range. This is also good because you will raise your HP and not get many combat levels.
Time to Train Range
Wear your short bow and your 6000 arrows. You can wear your full iron armor and cape. Put everything away. I have a picture above of the hobgoblins. Try and get to the area that I was at. If your stand here and range, the hobgoblins won't get you. You won't have to pick up your arrows. If you finish your arrows and you aren't level 40 range, you can go pick up arrows because lots of people range and don't pick up their arrows. Now you can wear your green d-hide chaps and vambraces.
Mage (Optional)
The reason this is optional is because you're only doing it to teleport. If you don't want to teleport you are done. If you are going to teleport, you should equip your air staff and have mind runes in your inventory. Don't wear any armor. You won't need any food.
Go to Varrock castle and find the stairs. Don't go up the stairs, but if you look behind it, you will see a monk of Zamorak. You will be attacking this with only air strike until level 25 mage. You will be allowed to use Varrock Teleport.
Congratulations. You are now a strength pure. You should wear iron full helm, iron plate body (or chain body), green d-hide chaps, green d-hide vambraces, anti dragon shield, rune scimitar, cape, and boots. When PKing, you should have 1 strength potion, 1 fire rune, 3 air runes, and 1 law rune for teleporting, and the rest of your inventory are lobsters.