Depends on what you're looking for and what you wanna do. Do you wanna level and play casually, or power your character to 60 and do lategame content? Are you interested in world pvp or battlegrounds? Will you mostly play solo or with a group? etc..

Mages are probably the best DPS class in the game for PvE and have incredible quality of life perks (teleports and free food / water are insane lategame). Great slows and CC, great AoE, and super fast gold farming. They're insanely good at group PvP but worse at 1v1s than priests and warlocks. They're also not as gear dependent, which is great because getting raid gear on a mage is absolutely horrible.

Warlocks are the undisputed kings of solo PvP and the best scaling class in the game when BWL and beyond raid gear are out. Their quality of life is a lot lower because you need to spend a lot of time and inventory space constantly making sure you have soul shards for some of your abilties. Also having the right pet out can be tricky in PvP situations where you might not be given the time to resummon. Farming raid gear as a warlock is also a hell of a lot easier than as a mage.

Priests, obviously you can be a healer which the other two classes can't. You have viable specs for healing (disc / holy) as well as a very strong spec for PvP (shadow). Shadow priest is second only to warlock for solo PvP strength, but is pretty terrible overall as a PvE DPS class. For PvP it's very much an attrition based playstyle with low damage, which some like and others don't. Disc / holy priest is the defacto healing class in classic WoW for good reason. As a healer it's also super easy to find dungeon groups.

For leveling Warlock is by far the fastest and the easiest. Mage can be fast if you know what you're doing but very slow if you don't. Priest is good at leveling but you spend the first 40 levels placing dots and then using your wand, which I found insanely boring but that's a matter of opinion