(I can't speak to the current state of the game since I last played during the Cataclysm era, but the points I want to make aren't things that can be seriously affected by the usual economic fluctuations so they should still be valid.)
Time is the only real currency that really matters in MMORPGs.
When you have a gathering profession such as Herbalism, you are trading your time spent wandering around picking flowers for gold.
Crafting professions, on the other hand, trade time for gold by only being able to craft a product so many times per time period. For example, Alchemists can only do a transmutation every few days. Crafted products that aren't time-limited are rarely profitable, unless you play the auction house game and know what words like "arbitrage" mean. (This is fun for some people, and there's nothing wrong with that!) Levelling up a crafting profession is break-even at best. (Again, unless you play the auction house game)
Now, let's talk about high-level players. There are tons of them now, there have been for many expansions now, and there will be until the servers are turned off. High-level players earn more money in an hour than a low-level player does, so they'll pay more for an hour's worth of Peacebloom gathering than a low-level player could.
I say that a new player (without an existing pool of money to draw from, like a friend) would be smartest to take two gathering professions. Take advantage of this money gap! If you take a crafting profession, you have to compete for materials with high-level players and their huge wallets. If you take one crafting profession and feed it with the outputs of your gathering profession, you are throwing away money that a high-level player would have gladly given you in exchange for your time.
Money isn't everything. The whole point of playing is for fun. Keep in mind that you may (or may not) find one or more of the following things fun, even though they do not optimally increase your income per hour played:
- Searching for deals on the auction house.
- Stat boosts from some professions.
- Unique abilities or cosmetic items that you can only equip if you have a certain profession.