Probably cooking, you can actually make money on your way to 99 cooking things like lobsters. XP/HR depends on what youre cooking but you can easily get 1m xp per day legitimately.
The cheapest skill is Dungeoneering. The fastest skill is Herblore.
The cheapest and fastest is probably cooking Rocktails, you make around 50GP each Rocktail so you are making a small profit. Hope I helped.
As for me, the cheapest and fastest skill to level-up is Fire Making. Cooking is just the second skill for me as the cheap and fastest skill to level-up. However, if you are just looking for the type of skill which is the fastest to level-up then that's Prayer but it comes with a huge cost.
Cooking, Fletching and Firemaking are all fast & cheap. Woodcutting is fast as well, takes 2 weeks for 99 with ivy + you profit from all the bird nests.
Firemaking, once you get to level 83 you can go to jadinko lair which is free and the xp is about the same as doing bonfire yews. Cooking did break even and sometimes profit with rocktails, but idk.