Before I get too into these professions, let me just state that I'm not really Basil Berntsen's type -- I'm not gold capped, I'll never be gold capped, and I have no desire to be a Warcraft billionaire. A lot of people take professions just to make money, but I'm more than happy with keeping enough cash on hand to pay for my repairs, buy some gems or potions when I need to, and buy cold weather flying for all my alts.
When I choose professions, it's for the leveling and end-game benefit. A little cash along the way is always great (and really, you can make a little bit of cash with most of your professions regardless), but many professions will actually wind up increasing your end-game DPS. And really, isn't that what us shadow priests really care about in the end? Melting (Dawn Moore's) face?
I'll be brief when discussing mining, since it really... just isn't ideal for shadow priests. It's a gathering profession, and as such, has the potential to be a great moneymaker for you if you put in the time to farm. Every time you increase your mining skill past a multiple of 75, you get a new rank of Toughness. When you hit that magical 450 mining mark, you gain 60 points of stamina from Toughness (Rank 6). Those extra points of stamina are great for tanks, but do nothing for your priestly DPS.
You can't wear mail or plate, so why would you choose to spend your time in WoW making it? Blacksmithing is an expensive profession to level, especially if you're not a miner. And I know you're not a miner, because I just told you in the preceding paragraph not to be a miner. If you crave irony enough to be the best cloth-wearing blacksmith in all the land, you'll at least be able to add an extra gem slot to your bracer and glove as a blacksmith-only bonus. Provided you use Runed Cardinal Rubies, the benefit to mastering blacksmithing is a 46 spell power boost.
Again, I'll be brief -- why dedicate yourself to crafting leather gear you can't even wear? I will note that leatherworkers do get a valuable leatherworkers-only "enchant" that's worth 76 spellpower. Anyone can get a +30 spellpower enchant off the auction house, so the net end-game benefit would be 46 spell power, just like the equally useless blacksmithing.
A gathering profession that goes hand in hand with leatherworking. Apparently, skinning animals gives you a better idea at how to kill them, because the profession gives you a slight boost to your critical strike rating, maxing out at 40 points of crit when you level it to 450. That's an end-game benefit of approximately 30 spell power.
I almost hate to lump herbalism in with the previous four professions, because it seems so useful. Herbs -- even lower level ones -- can sell for a lot of money, and some even give you a temporary buff when picked. There's no DPS boost associated with the profession, however. Each time you level your herbalism skill past a multiple of 75, you get a new rank of the herbalism heal-over-time ability, Lifeblood. The profession bonus is good for a class without a self-healing ability, but it's absolutely wasted on a shadow priest.
Those five out of the way, let's look at the professions that hold a lot more benefit to shadow priests, and really, casters as a whole.
This is a simple profession -- you take the scraps of cloth you find off enemies, convert them to bolts of cloth, and then make cloth-based armor to equip and bags to hold your stuff. If your Warcraft playing style leans on being especially self reliant, tailoring is a great choice.
Pros: If you don't have any alts or guildies to help you out, you'll love being able to make your own bags. In addition, you'll be able to gear yourself up with some pretty decent clothie equipment, like the early-game Spidersilk Boots or ICC-level Deathfrost Boots. In the end game, you have access to the cloak "enchant" Lightweave Embroidery. It has an internal cool down of 45 seconds, which is worth an average of 75 spell power depending on how fast you fire off spells. (A recent analysis of my own logs showed ~25.7% up time in Icecrown Citadel.) Without specializing in tailoring, you could still enchant a cloak with 23 haste, so tailors get a ~53 spell power benefit from their profession.
Cons: If you're looking for a lucrative profession, tailoring most definitely is not it. A lot of the stuff you have to make to level up is absolute garbage that won't sell for anything on the auction house, and if you want the best end-game craftables, you can always find another tailor offering their services on [2. Trade]. You used to be able to make a little bit of extra coin selling extra pieces of specialty cloth (like Spellweave), but since they're no longer on cooldown, the market has dried. And, if you're spending your time leveling through instances, you'll find the drops there tend to be appreciably better than what you can make yourself.
Specialization: If you do decide to be a tailor, you'll want to choose a specialization. You can do this by completing a quest in Shattrath, provided you're at least level 60 with a 350 tailoring skill. There are three specializations: Mooncloth, Shadoweave, and Spellfire Tailoring. The only end-game benefit to specialization is getting an extra piece of Moonshroud, Ebonweave, or Spellweave as a bonus each time you make one. Specialize in whichever of the three sells for more on your server's auction house (often Spellweave, but prices do fluctuate).
If you're going to become a serious end game raider, you're going to need elixirs and potions -- and lots of them. What self-respecting shadow priest doesn't raid without a Flask of the Frost Wyrm? Who doesn't pop a Potion of Wild Magic to squeeze out a little bit of DPS every now and then?
Pros: There are a bunch of great benefits to alchemy. You can make potions to boost your intellect and spell power. You can make your own trinkets as you level. But best of all, you get access to Mixology, which boosts the effect and duration of your flasks. At the end of the game, that's worth an extra hour and 46 spell power when you use a Flask of the Frost Wyrm.
Cons: Alchemy is heavily dependent on access to herbs, so you'll probably want to level it alongside herbalism. And, as discussed before, herbalism doesn't offer an end-game DPS benefit. Of course, you don't need to be an herbalist to be an alchemist, but the profession gets very expensive if you're buying all your own materials.
Specialization: This time, the choice in Shattrath is this: Potion, Elixir, or Transmutation Master? I prefer potions, since I go through two a fight and the market for potions on my server is very seller friendly, but the correct answer is likely "whatever has the highest percentage profit margin on the auction house." In the end, the choice is up to you.
Pros: The "main" job of scribes is to make glyphs, and some sell for high profit margins on the auction house, making inscription a good way to make money. In addition to glyphs, you can make your own Darkmoon Decks (to create somewhat useful trinkets like Darkmoon Card: Illusion) and off-hand items such as Faces of Doom. The profession works well with enchanting, because you can make the vellum essential for selling enchants on the auction house. The end-game DPS benefit, however, is access to Master's Inscription of the Storm. It allows you to skip the Hodir rep grind and gives you 46 more spell power than the shoulder enchant available to non-scribes.
Cons: You need to mill herbs to make ink, so you'll need to be an herbalist to get the most out of inscription -- or, at the very least, have an alt or the cash to obtain the herbs.
Pros: Enchanters are able to improve most any piece of gear they pick up while leveling -- non-enchanters would find this prohibitively expensive during leveling. Further, enchanters are able to disenchant gear for materials, which often sell for more (and sell far easier) than the equipment itself. You don't need a gathering profession to be a successful enchanter, which is a notable benefit -- the profession is pretty self-sufficient. Enchanters are also able to enchant their own rings with +23 spell power, which puts it on the same +46 spell power level as most professions.
Cons: The profession is notoriously difficult to level from scratch, requiring you to make a number of near useless enchants. Also, recent changes in patch 3.3.3 make it far easier for non-enchanters to obtain enchanting mats, which drove down their prices.
Pros: There's a significant "fun" factor to engineering as a profession: You get to make pets, unique mounts, teleport, and can even access your bank and make repairs from anywhere. There are a number of engineer-only improvements that you can make to your gear: Springy Arachnoweave for your cloak, Hyperspeed Accelerators for your gloves, and Nitro Boosts for your boots. The DPS benefit from those improvements is hard to quantify, but it's somewhere between 40 (if you normally use the Icewalker enchant) and 56 (if you prefer Tuskarr's Vitality), subject to user error.
Cons: Some engineering schematics require association with the inferior gnome race. It's hella expensive to level due to its reliance on mined ore, and some of the coolest engineering toys still require thousands of gold to make even once you have the ore. And most of those great engineering tools for boosting your DPS are "on use" items, which complicate rotations, introduce human error, and frequently result in suboptimal performance.
Pros: People who jewelcraft as they level through the game will have access to some decent jewelcrafter-only trinkets and will be able to make some pretty decent rings and neck pieces. Cutting gems can be a money maker -- level 80 raiders are constantly in need of gems for their newly acquired gear. Once you level your jewelcrafting to 370, you can make your bind-on-pickup Jeweler's Gems like the Runed Dragon's Eye. You can put a maximum of three of these into your equipment; since each is worth 16 spell power more than the equivalent Runed Cardinal Ruby, the profession carries its own unique 48 spell power buff.
Cons: Jewelcrafting stinks to level without access to large amounts of ore, so it's either going to be an expensive profession or one that requires a lot of mining. And what did I just tell you about mining?
So, what's the bottom line here? Most professions are standardized to 46 spell power, but a few stand out as (slightly) better: Tailoring (53), Jewelcrafting (48), and Engineering (40-56). Now, to be sure, a lot of raiding professionals are going to choose Engineering and Tailoring, simply because of their DPS advantages over other professions. That's fine for them, but remember, the net DPS increase you'll see from min-maxing your professions probably may not be worth the time and effort. Just know the benefits and costs of each profession, and choose what improves your game experience the most.
I still think the most advantageous (and smoothly integrated) combination for shadow priesting is Tailoring/Enchanting, though I admit I'm a bit biased. The two have great synergy, and provide a near optimal end-game bump to your DPS. But it's not the only "right" answer to the question, "What profession should I choose?" Let's put the question out there to you, the super-experienced, all-knowing shadow priesting audience: What professions did you choose, and why? And are you happy with how it turned out?
Hunger for more information about bending the light to your advantage? More interested in watching health bars go down than watching them bounce back up? Think it's neat to dissolve into a ball of pure shadow every few minutes? The darker, shadowy side of Spiritual Guidance has you covered.