Choosing professions

Hello, I am not too new into wow, but also not really experienced. I only had a character, druid that kind of profited from skinning for gold making and now I made mage and I am not sure what professions would be mostly neat for making gold and making profit so I picked something where you can buff yourself and sell them. But I also I thought it could be neat to enchant pieces of armor and weapons. My question is it necessary to have herbalism and alchemy together? or I could , for example, unlearn alchemy and make gold with herbalism only

Yes, you can make gold with herbalism only, it's just that they go together well. Like mining and blacksmithing. But you can have herbalism for easy money and another profession that you like or find useful.
Option that first comes to my mind is Tailoring - doesn't need a side profession. You only need cloth (and some other junk sometimes) to craft most items you'll need for leveling the profession. Nice bonus is that you're a mage and you can sometimes craft something nice to replace that 20levels old item and level up your profession along the way.
Enchanting is nice and profitable, but a pain in the *** to level if you don't have lots of gold.
Rest of them are either not quite mage-like, like mining, it's easy, profitable since the start, but it's benefits to a mage are next to none (stamina). Others are good and useful like Engineering but that's expensive and not as profitable as others, only for later content where it has some nice benefits.

I see, so all in all enchanter would be really heavy for gold, yeah then It could be something I will do later on, for now I will stick with what I have then and see what I can do, thanks a bunch if anything !

Enchanting is awful to level up, and will cost you a ton of money which probably you will not have returned anytime soon. Endgame enchants sell really cheap and the profit is really small.
If you are starting out, you should stick to gathering professions to make gold, like mining, skinning, probably herbalism too.
The only trick that can make enchanting profitable quickly is to just pick it up and keep it at 1, which will allow you to roll "disenchant" in dungeons on any item (even ones you can't normally disenchant due to low skill level).

Best profession to make gold is Inscription by far, especially if you are low on gold. You buy one ink for 6-7g, paper 1g and sell it for some 15g. Just print gold.

Then I'd say Alchemy, either Potion master or Elixir master. Good for start too and additional benefit is when you already got gold going you can start making Darkmoon cards and cash in monthly on trinkets.

Then, I'd say Enchanting. Big thing about it is you don't have deposit costs on enchants, so you can spam post them without undercutting.(same as Inscription, big reason why it is so start-friendly)

Gathering professions - you have only as much time as you have, but buying reagents-crafting-posting on AH scales to infinity, so you can spend 20mins a day on it and cash in tens of thousands each week.

Biggest thing about all this is - I see so many people saying "omg I posted my stuff and its been 12hrs already - NO ONE IS BUYING IT!". Yes, that's how it works, unless you undercut - which I DONT recommend. You need to think in weeks instead.

My experience with inscription the past year was that in theory you would be printing money while in practice glyphs don't sell.

Well, I sold all I ever made and I have made thousands upon thousands. What do you mean by "glyphs don't sell"?

I remember making a shitload of glyphs and only one or two would sell every day. I would have to repost most of them forever and some of them I ended up wiping my ass with.

Hmm, I make stack of each(each - meaning glyphs that PvE and PvP specs use) and its all usually gone within 2 weeks.