I am interested to know what you have gone with for professions and what has worked well for you.
As I’m leveling I’m going skinning/mining at the moment (and selling materials on the AH). It’s not bad - my end game goal will be to drop skinning for engineering eventually.
What have you gone with and why?
Tailoring for early game bags/making bags for alts. Made some nice robe sets too for my warlock and priest for later on as well. Then of course Archmage robes right now… after all that is done will most likely drop tailoring for herb and drop skinning I used to make my mount cash for alchemy. These two together obviously pose a synergy combo to provide me with all the potions I need for raiding and other goodies
All of them. It’s called alts. But enchanting skinning on the main. Got to DE stuff when soloing and low competition on skins comparatively.
Herb and alch, the way I figure it there will always be a market for it. You can go into pug raids and upsell the $@#$ out of them. Soon you will be so rich, you will have a camp fire made out of warden staffs.
Skinning/leatherworking. I went leatherworking because I’m resto and planning to stay that way at 60. At least this way I’ll be able to craft a few intellect leather pieces. I’m also skinning everything I can get my paws on for money. I’m two levels away from 40 and still only about halfway to mount money. I need to buckle down and actually go gold farming more.
Alchemy/Herbalism on both my Mage and my 44 Priest. Both are 300/300.
Transmute income is 6-10g per… every 2 days. Twice.
Made 750g in 2 days last weekend farming herbs and selling raid pots (greater fire protection, major health, major mana, mongoose, arcane elixir) and got epic mount. I just picked up Greater Arcane Elixir recipe the other day as well. Profits should continue.
Priest will have epic mount the moment she dings 60. Always prepared with my own consumables.
People will sooner or later have their tailored gear and enchants… but they’ll continue to buy potions.
No complaints here. For years I went tailoring/enchanting but don’t regret passing on it this time around. The return has been much better than crafting an epic robe or selling bags in a flooded market.
Everything but engineering at the moment. All my toons have at least one gathering prof, some have two. This toon has Tailoring and skinning, I’m leveling enchanting on another account so I can 'chant everyone’s gear without chasing down an enchanter. I’ve been a little slow leveling tailoring, made my first silk bags yesterday.
I imagine a couple toons will powerlevel engi at 60.
Herb + Mining until level 35.
I banked 100% of the Herbs for use with Alchemy down the road, and sold the raw Ore on the AH to help make some moneys while leveling. At 35 I ditched Mining and picked up Alchemy and used my banked mats to get me to 220ish without spending a copper piece on Herbs. I continue to pick up whatever herbs I can find and plan on swapping Herb for Engineering after 60 for all the usual reasons.
Engineering/Mining…every toon.
Why not add more CC/skills to my toolkit? Yes, please!
And…have you seen the prices on ore and bars! Gold mine…pun intended.
Always be gathering, has worked since Vanilla, and still works in Classic.
So… basically every one of my guys has at least one gathering profession.
Alting.
Love alchemy and skinning the most so far. Tailoring, too. Holding off chantz for now.
Blacksmiting and mining. Because apparently I’m a masochist.
lol I did that in vanilla, never again. You’re definitely a masochist.
For extra Masochism I’m also leveling a prot warrior.
On this toon, Skinning and Leatherworking - Practical to make my own armor and arrow quivers.
My NE Warrior has Mining and Blacksmithing so she can make her own gear, and my brand-new Tauren Druid has Herbalism and Alchemy for practical purposes (Bear form gets extra boosts from buffs, if I understand correctly, and Tauren get a boost in Herbalism). My cloth-wearing toons tend to learn Enchanting and Tailoring for survivability.
As a mage I went with enchanting and tailoring, easy things to make and then disenchant them. Sell the supplies or use them.
Depends on your class imho and/or what kind of activities you do.
Clothies and tailoring go well. Each class has a craftable and very excellent robe. NTM Bags galore!
Any class that uses mail and melee weaps can benefit from mining/BS.
Leather working and skinning are good choices for rogues, druids and hunters/shaman, who start wearing leather but can learn mail later on.
If you want to just make money, gathering professions are good. Herbalism (and alchemy) are pretty profitable and so is mining and skinning.
If you PvP then Engineering/ mining is your optimum choice. Engineering has many fine and fun devices that can be used against your enemies 
Enchanting really isn’t all that significant until end game and it is a bit pesky to level.
All the professions.
I love dabbling in the AH so between my husband and I, we have all the bases covered.
Skinning herbing on main will drop skinning aometime after 60 for engineering. ALT WILL have mining skinning. Then drop skinning also for engineering. Will probably do another alt with alchemy skinning then switch to …drum roll engineering.
No point in selling raw ore. Blacksmiths and engineers can’t use it. Others miners who can gather their own ore would have to buy it to smelt it. You should smelt it first, then sell the bars.