Why? My sister's nerd ex-boyfriend gave me a little 10-day trial slip he'd gotten in the game box and I decided to try it out. I liked it and eventually bought the full classic a few weeks later.
Race? Nigh Elf male. My very first character and still my main. Never gonna give him up, never gonna let him down, never gonna reroll or delete him. I just thought that the night elf males were much better looking than other male race variants and didn't really think rolling a female character as a male would be appropriate for my first character (and I thought the females were weirdly disproportionate at the time).
Class? Warrior. I've also always liked warriors in other games (extremely simple to play, hit like a truck, and hard to kill... usually).
Faction? I preferred the Alliance because they seemed less monstrous and evil. But, after I got BC, I liked the look of the blood elves, despite their maniacal lust for power and destruction. Guess aesthetics play a large part, though I do enjoy goblins and draenei. But only certain race-class combos work for me. I like goblin casters, especially locks (dem red and yellow eyes). I like draenei tanks and shaman. I like night elves and worgen as anything, but females fit caster armors a bit better.