Which druid profession is best in the long run: Skinning/Leatherworking or Herbalism/Alchemy?
I'm looking for the profession that will be the best for me to have once it's developed pretty high. As a druid will it be more beneficial to use the alchemy approach, as consumables will likely cost a lot at the AH? Or will leatherworking make me so much money that it won't make a difference? Alchemy seems the most useful now and in the long run, but is leatherworking a better route for the money?
It depends on what you're looking to do.
If you're looking for min-maxing your stats, you'll want to ditch either Skinning or Herbalism entirely from that list. The passive bonuses from those professions are far below what the other professions offer.
If you plan on tanking, Mining is the only gathering profession worth anything. Still a bit below what you can get out of the other professions, but 60 stamina from max level Mining is a very good passive bonus while being able to retain a gathering profession. However, if you don't plan on tanking, Mining is not ideal, and unlike the other professions, you can't "switch" the bonuses per spec (like using different Dragon's Eye cuts as Jewelcrafting, for example).
In terms of Alchemy vs. Leatherworking, both offer their own unique benefits.
Alchemy will provide you with increased flask duration and effect (2x duration, and 1.5x the bonus effect). Alchemy also provides you with the means to create said flasks (and potions that you'll inevitably use). Even if you're forced to buy the materials raw, you'll end up saving by making them yourself rather than buying the finished product on the AH. Additionally, as alchemy, you have the ability to learn how to transmute epic gems on a 20 hour cooldown (basically 1 a day).
Leatherworking will provide you with a unique-to-leatherworking wrist enchant, either attack power, spell power, or stamina (DPS, caster/healer, and tanking choices, respectively). Additionally, you can make extremely cheap leg enchants for yourself only. While they are no different than the ones that you can make for others in terms of stats, the material cost to enchant your own legs is very low comparatively. Lastly, you can learn/make the epic leatherworking pieces in the end game which are expensive to craft but also very useful pieces to multiple class / spec combos.
In terms of money making, your best bet is going to be Jewelcrafting, Alchemy, or Inscription. They have the items that people always come back for and need on repeated and frequent basis. Note that Inscription will likely not be in this category in the upcoming Cataclysm expansion, as recent news has indicated that Glyphs made by Inscription will not be constantly replaced, but rather a 1-time-learned-forever-retained thing.
In terms of min-maxing stats, it's slightly dependant on your class/spec, but your best bets are Jewelcrafting, Blacksmithing (combined with Jewelcrafting), Tailoring (for casters/healers), and Engineering (for DPS classes, though the utility gain through Engineering is useful for everyone).