Hey all,
So lets start with some ways. I'll add more when I find more (:
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First I'll start with free world total beginners that want to make easy cash in little time.
The best way for this (my opinion) is mining:
You spawn in lumbridge with all of your stuff blablabla.
Drop everything except your pickaxe and move to Varrock.
At the south-east and south-west are mines. Choose one.
I'd advise the east mine since you won't get to much dmg from the lvl 3 rat there. At the west mine is a lvl 6 mugger that can be very annoying (:
Mine copper/tin, you can bank it at Varrock west bank or you can just powermine and drop all the crap because it isn't worth a dime (:
Do this until you are level 15.
Now go mine iron.
G-E price of Iron: about 222
If you do 27-28 iron a load, you will make 5994 (27) or 6216 (28) coins a load. So this would be the easiest way to make some quick money to start of playing.
You will have enough money to buy food and armor to level.
You will have enough money to buy equipment for fishing, wootcutting etc.