You can customize the skin tone, hair, and face of your avatar. I can’t guarantee you’ll find one you’ll like, but you’ll probably find one you hate less.
Seems to me Draenei would make decent caster/melee types, such as shamans, paladins, or hunters. I made my Draenei a shaman, but more because I liked the class than because I liked Draenei. Draenei just gave me the opportunity to play a shaman on Alliance side, as prior to the expansion they were a Horde-only class.
This will really depend on your server and how you want to play, though. I don’t think you should worry much about what classes are in demand. Whether you decide to group up or solo, I think you should pick a class you enjoy playing. It’s a long way to 70, and it’s little consolation that you’re in demand if you can’t stand the class you chose. You’re also going to be better at your role if you enjoy it.
I came from FFXI, where group play is the entirety of the leveling process. Maybe this biases me, but I’ve found that the average WoW party sucks. Damage-dealers have little grasp of hate management, and will often tear mobs off tanks. Some won’t attack the same mob the tank is, and will pull hate onto themselves with a single spell. I haven’t seen many tanks that can handle multiple targets. Healers seem to be the only class that performs consistently well.
When I started WoW, I joined up with other FFXI refugees and wound up duoing with a FFXI buddy to level 70. I’m glad I did this, because if I had to party with the average WoW player, I’d have quit months ago. Knowing I have the option of soloing makes me much less tolerant of incompetence.
You can grind on whatever you want, or you can do quests. If all you care about is leveling, then you can do either, but if you want some fame and money and gear, then quests are the way to go.
WoW’s quests are pretty good at disguising the fact you’re grinding. About a third of the quests are quota quests: go out and kill N of mob type X. There are enough quests that you can be selective in which ones you do. My priest alt, for instance, is at level 37 now, and I avoided all the quests I hated the first time through, and my quest log was almost always full.
The only difference I’ve really noticed for lower levels is you level faster. Quest objectives, difficulty, and opportunities are pretty stable throughout the game.