As for money in the end, they're all about the same.
But, early on your best bet is probably Mining > Herbalism > Skinning.
Mining you can make good money from the start selling copper bars.
Herbalism, once you get up around 100-120 or so, you can start making some decent cash, and it only gets better from there.
With Skinning, it starts off really slow, but you obtain leather in mass quantities doing killing quests and such, unlike the other two, where you have to constantly search for resource points. But, the leather sells for less early on than the materials gathered from mining or herbalism.
Once you get to getting Heavy Leather and, even more so, Thick Leather on a regular basis, then you can start making some good cash with Skinning.
So, Skinning is slower to get to the good stuff than the other two, but they're all still really good for making cash.