The easiest gold doesn't actually require lots of characters. You can make plenty of money by simply playing your characters, selling surplus points, and avoiding unnecessary expenses. The benefit of having a bunch of characters at max level is actually that you can simultaneously exploit every profession. The way profession-based gold making usually works is that the more time you spend on it, the less gold you make per hour -- it's the law of diminishing returns. Having more professions allows you to focus on the low-hanging fruit on more trees.
What to aim for
The ideal goal would be to have one of each profitable crafting professions and possibly some farming professions. There are eight crafting and three gathering professions. First off, even though it's common sense to combining crafting and gathering professions, you usually won't want to. Other than for mining and blacksmithing, this advice is for people who don't plan to make money from their professions. You will save a ton of time if you make your blacksmith a miner, with all the smelting you'll do, but other than that, your skinning and herbalism farming skills should be on a single character so you can collect twice as many types of goods when you have to farm. Also, alchemy and inscription share materials, so it can be more convenient to have them on the same character.
For the crafting professions, you can safely ignore engineering. It's an awesomely fun toy but doesn't make much gold at all. This leaves seven professions you will want access to, eventually. You'll notice that assuming you don't double up any professions, you're going to have five characters in use. What should you do with the others?
For now, nothing. Adding more copies of your gathering skills won't help you unless you can somehow play more than one at a time, and adding a copies of crafting skills will bring you far less of a benefit than the original did. Focus on getting your first copy of all your target skills profitable before you start making second copies for cooldowns.
Now that you know approximately where you want to be, how do we get there? Which professions come first? Powerleveling a profession can be extremely expensive, so you're going to want to focus your means on the best possible short-term returns. Every profession leveling decision you make should be based on how long it will take you to recoup what you spend on it.
Personally, I'd start with enchanting and jewelcrafting. They're relatively cheap to level if you take your time, and enchanting reduces the cost of leveling other crafting professions down the road, since you'll be able to disenchant the gear you make. Jewelcrafting and enchanting also complement each other in many different points during the leveling process, mostly because it's often cheaper to buy the ore needed to craft disenchantable JC crafted items than it is to buy the enchanting mats you'd need to level. This is can also be a significant source of revenue for you before you get all the way to Cataclysm crafting levels -- you're not the only person leveling enchanting!
Next and possibly before those two is inscription. It's either going to be very profitable or a little profitable, but either way, it's dirt cheap to level. You will be using a lot of older inks, and while the first person to level inscription had to mill herbs from old zones (which are incredibly expensive), you can simply buy Blackfallow Ink by the stack (or have someone mill it for you) and trade it in for whatever inks you actually need. Once you're capped, you'll want to check the glyph market, but it's probably low profit. If it's not, then start learning glyphs, and whether or not you can make glyphs work on your realm, you should be milling and selling inks for a profit -- not just the current ones, but the old ones that a bunch of people don't seem to know you can trade down to. Also, sell Mysterious Fortune Cards.
Once you have these down, my next recommendation would be one of the gear crafting professions. Blacksmithing or tailoring are cheaper than leatherworking to level, and BS has some materials in common with JC. You might be able to find some niche transmog or leveling gear markets on your way to the current stuff with a gear crafting profession; however, the majority of your profits from these types of professions are going to be selling current items. You want to make PvP blues, leveling greens and blues, and any item enhancements or profitable odds and ends you can find.
If you're literally starting with nothing, then farm until you can at least get one profession going. Always spend your time on crafting first when you can, and farm only when you run out of profitable things to do with your crafting. As you farm less, though, remember which farmable items (like lower-level leather) are insanely expensive. It can be a lot more gold per hour to go back and farm for other people leveling through BC or late vanilla tiers of mats than competing for the same heavily farmed Cataclysm nodes. Whenever you're deciding how much something cost, remember that the mats are worth what you could have sold them for.
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