The best is probably WoodCutter or RuneCrafter. Even if you can't craft Nature runes on f2p, you can still make loads of profit with air runes and stuff if you get like 80+ Runecrafting. With Woodcutter you need like 70+ Woodcutting to make some actual profit, because Yews cut slow and people have higher levels.
With R/C I would imagine an income of about 40k/h max. With yews, probably about 30-50k/h max.
The greatest thing about F2p is that you don't have to worry about ban rate, so just run like 3 accounts at the same time w/cing and make a good 120k/h+ and do it 24/7
Calculations:
120000x24 = 2.88m per day
2.88 x 7 = 20.16m
Thats $20 every week. and eventually if you get like 5 comps you can make a good $120 every week from doing nothing. Even more if you invest in stuff.