WoW Classic contains a wide variety of professions. Some of the professions fits better with certain classes or play styles (PvP/PvE). This guide will give you insights on which professions you should consider if you want to do the PvE end game content.
Tailoring are by many considered as mandatory for mages and warlocks if you are a serious raider. After the Zul'Gurub patch a cloth set called Bloodvine is obtainable. The Bloodvine set gives a total of 4% hit, 2% crit and a total of 83 spell damage. Bloodvine is BiS for mages until AQ40. Even after AQ40 it is difficult to obtain the BiS items which replaces the Bloodvine set. Tailoring is required as the 2% crit bonus is only received if you have lvl 300 tailoring. After obtaining items that are better than Bloodvine you can choose to change to a different profession.
As for the second profession mages have a few options: skinning, enchanting, herbalism and mining are the most common ones. Skinning is useful as some of the materials needed for tailoring is leather. Skinning is also a good method to earn some money while you are leveling. Enchanting and tailoring is a very good fit as you can create green items with tailoring and disenchant the items to get mats for your enchanting. If you want your second profession to be most efficient money vise, your best bet are herbalism or mining. With herbalism you can gather materials needed by raiders. You can choose to keep the herbs yourself and save money, or sell them off to make a nice buck. Mining is always in demand as it is used to craft gear, weapons and create engineering items.