The two standouts are alchemy and engineering because those will be the source of most consumables you’re using. Alchemy will let you craft your own flasks and
Pozione del Potere Prolungato and give you two hour flask duration instead of the usual one hour. It will also let you make
Skaggl Potabile and
Pozione del Passo Celestes. Engineering lets you craft
Pilone d'Individuazione Fallimenti and item repair items like
Automartello.
Additionally, Engineering gives you access to some enchants that are useful in M+. The most obvious is
Carica per Cintura which allows you interrupt groups of mobs and is critical for big pulls in high keys. Another is the
Sottotela Flessibile which lets gives you a slowfall effect and can be useful in some dungeons with Z-axis elements.
Enchanting can also be useful because it lets you disenchant the (many) items you will get from M+ that aren’t useful. This can be a significant source of income if you grind a lot of keys, and it generate a modest amount of
Sangue di Sargeras if that’s something that interests you.
No other professions do much for M+ specifically, but it is worth mentioning
Court of Stars. CoS has several items distributed that give buffs if you’re able to use them. Each profession has an item associated with it; the usefulness of those items varies rather dramatically. Some of the items summon Talixae Flamewreath’s lieutenants and aren’t particularly desirable. Those professions are Leatherworking, Mining and Jewelcrafting. Some professions give buffs: Inscription and Skinning get movement speed (meh), Enchanting gets a damage buff (now we’re talking), and Herbalists get haste (winner winner). Alchemy will let you poison a flask that will kill Gerdo instantly at 25% health. The big ticket professions, though, are Blacksmithing and Engineering. Blacksmithing gets access to a trap that instantly kills one of Talixae’s lieutenants, and Engineers can use an orb that disables every Guardian Construct in the dungeon. The amount of time saved by these two items is tremendous, and not having someone in the party that can activate them is a significant impairment. Engineering is common enough that most groups will have an Engineer without trying, but Blacksmiths are rare. I have brought people to my Court of Stars groups specifically because they have Blacksmithing.
You can’t go wrong with Alchemy and Engineering, and Enchanting and Blacksmithing both have uses. The rest of the professions won’t much affect your M+.