Updated: Oct 27, 2018
The Barrows Brothers You can literally do Barrows with about 10k. Black Salamanders are dirt cheap, and Harralander tar is worth nothing.
Doing the Morytania Diary, the Hard or Elite diary, gives you teleports near Barrows, and is actually the most efficient way to do your Barrows trips. But, I would recommend buying the Barrows teleport tablets off the Grand Exchange. They're about 3k each, and anyone can use them. You'll need to bring a spade with you as well, and you will definitely need some Prayer potions and a little bit of food. The Barrows Brothers have a very low Magic Defence, so if you were to wear armour to Barrows, your best bet is to wear Defensive Melee armour. If you're not using the Salamander, you should also bring a ranged weapon along with a Magic weapon, where the range weapon is used to kill Ahrim, and the Magic weapon is for all the other Barrows Brothers.
The Slayer's Staff E or the Iban staff is a great low level option. Otherwise, higher levels can use the Trident of the Seas, or the Trident of the Swamp. So, the Salamander was doing really well and I wasn't even using any armour. So, I wasn't getting any attack or strength bonuses while I was fighting. I was doing 12 runs an hour at an easy 1mil per hour. At lower levels you might expect a bit under 1mil per hour, but with the combination of Rune drops, and things like the Ahrim's robe top, or the Karil's leather top, you really can make a lot o money here. Doing at least the Morytania Hard Diary also increases the loot that you get from Barrows. It doesn't increase your chance of getting an item, but increases the amount of Runes and other non rare drops, which really add up to the total. I'm sure even the lower level Salamanders will work as well, but of course your trips will be a bit longer and you'll need a few more Prayer pots and food.