If you want to gather a group for a hard dungeon in World of Warcraft, which two classes are you looking for first? Most people will probably answer "priest and warrior" to this question. If the dungeon is not so hard, or it is a lower level dungeon you visit with higher level people, all sorts of class combinations can work. But when the going gets tough, you better don't rely on a voidwalker tanking, healed by a shaman. Mages are probably the third most popular class for group invites, but priests and warriors are the "must have" classes.
Now that would suggest that priests and warriors are equally sought after. Unfortunately that is not the case, because of the 8 races in World of Warcraft only 5 can make a priest, but all 8 can be warrior. I don't know if that is the reason, or whether people just prefer warriors to priests, but warriors do outnumber priests on every server. On my server, Horde side (Horde only has 2 priest races), during the morning and early afternoon when people do mostly soloing and small groups, warriors outnumber priest 2:1. During prime time people log on their raid characters, and priests being very necessary in raids the number of priests goes slightly up. But still warriors outnumber priests 3:2.
So if you crave to be popular, with lots of people sending you group invites, you getting easily into any guild, and you being able to get a spot on your guild raids even if you weren't among the first to sign up, play a priest. I'm playing my priest more frequently now, he has basically become my main, just because it is so much easier to get accepted by other people when I play him. In the much rarer cases where people already have a healer and are still looking for a tank, I can always switch to my warrior. If my two level 60 characters were lets say a hunter and a warlock, it would be a lot more difficult for me to find groups, and I don't think I could have joined my new guild that easily, and getting taken to MC raids two days after I joined.
Now if your main purpose in life is getting lots of epics from raids, choosing to play a warrior becomes even less good an idea, unless you run your own guild or manage to become the "main tank" of your guild. In the list of popular classes for raids, warriors due to being so numerous are falling behind not only priests, but also druids and mages. Furthermore most guilds operate a loot distribution system which heavily favors one or two warriors over the other warriors present. That is simply a reaction to how the game works, the gear of your "main tank" plays a large role in determining the success of a raid. Thus if half a dozen warriors regularly participate in raiding, giving the main tank(s) the lion share of the loot advances the success chance of the whole raid more than distributing the loot evenly over all warriors. That might seem rather harsh and unfair if you happen to be a non-MT warrior, but most guilds prefer to kill more bosses in every raid by favoring a main tank.
All this makes me feel slightly uneasy. Playing a priest feels like me social engineering the World of Warcraft class system. It is totally understandable for a guild to selectively invite more needed classes, or for a group or raid to preferably invite the must-have classes. But that means that nobody looks at you as a person, but only as an avatar, a class / level combination.
Fortunately I do like playing priests. And as I play MMORPGs since 1999, always having had a preference for tanks and healers, I play my characters competently enough. But sometimes I really wish I could play my warrior more, for example in 5-man dungeons, in a good group, it is the warrior who sets the pace by pulling, while the priest is far more passive, reacting to the group members health bars and not taking much initiative beyond that. As I said, often I like staying back and healing, but sometimes I'm watching some less competent warrior pulling very slowly and / or badly, and wish it would be me running the show. So I can see the dilemma for somebody who starts on a new server and happens to like other classes than me. Do you choose the class you prefer for soloing, or do you play the class which will get you into groups / raids / guilds most easily? If you have the time, I'd recommend leveling up a priest first, getting your network established, and then making an alt of whatever class you really like to play when alone. That is the disadvantage of massively multiplayer games, the best course of action doesn't depend only on you, but is a compromise taking into account what the other players do as well.