i'm not sure about f2p really because i was always p2p but anyways, my main idea about making money in rs is pvm, but you can make some good money with some dedication too. there is this really good way to make money without high requirements.
method's name: bone running
requirements: 50 construction, move your POH (player owned house) to yanille,home teleport tablets,27 bones (depends on the other guy) , the whole thing will be in w31.
explanation: well, it takes some time to explain but i'll try to make it short. i think you know that players train their prayer there by offering bones on gilded altars
http://runescape.wikia.com/wiki/Gilded_altar, so the main idea is that they need to train as fast as possible, which means they will need someone to do the banking for them, you will be that someone. to avoid getting scammed people ask the bone runner to bring 27 bones of his own so that they could trade them with the noted bones they have in bag, ofc you have un-noted bones, usually the price is around 25k-35k per trip (some people might even pay 50k but that is REALLY rare) so that could get you around 2m per hour (almost 50 trips) which is pretty decent considering the low requirements.
the process in a simple way: get 27 bones(dragon bones in most cases) and home teleports
---->enter the house that your client trains in
---->trade your un-noted bones with their noted bones+the cost of the trip
------> go to edgevile\alkharid(best choices imo) using the ammy on the wall in the next room
------>un-note the bones
----->teleport to the house again
-----> trade the bones (like step 2)
after you get some money from this method i suggest that you get your combat levels up to 80's and dung to 85 and kill frosts for their bones for a while, this will help you get your levels high and will get you good cash. it is recommended that you have good gear when you fight them and beware of the orb, because it can cause alot of damage
http://runescape.wikia.com/wiki/Frost_dragons after you get the money for prayer 95\herblor 96 and high end gear, start bossing and get rich.
*note that i haven't played in like 2-3 months so the prices and the effectiveness of these methods might have really changed.but i think it should be fine like that.