I need to answer this one in two parts, because I consider myself to have two answers to it. The first class I ever rolled was a Paladin, and he was Human. Unfortunately, he hadn’t completed any quests before I got a message from the guys who got me to play in the first place; “Um, sorry. The guild is Gnomes and Dwarves only.” It took years for me to ever level a Paladin and I blame that moment. I kid, of course…about the blame part anyway.
So having answered the question, it doesn’t really seem fair that a class I couldn’t even do a quest with would be my first. That’s why I consider the class I rolled right after to really be my first. My Priest. I read up on the class (since my buddies needed a healer and I could at least take a shot based on my City of Villains experience), and WoWWiki said something to the effect of “if you can handle the blame for everything, then choose a healing priest.” So I did. He started Herbalism/Alchemy and took on all that the game had to offer. He was Holy and had no trouble healing in the Deadmines, but got his butt kicked while wandering Ashenvale.
Prior to dual-specialization many people went Shadow and then at level cap flipped to Holy or Disc in order to heal. My first class taught me what would be common for me in every character I made afterwards, and that is that there was no such thing as dual-spec or respeccing as far as I was concerned. I took the spec I wanted out of the gate and I rode it to the finish. In the case of what I consider to be my very first class, I’ve ridden 90 levels as Holy and spent a fair share of that time question. But I’ve been in the dungeons, too. Heck, Tum might’ve even healed you once or twice.