1. Your looks depend on your equipment and race. BLMs wear robes and stuff, and I don't think there is any gear to make you look like Vivi.

2. I think DRGs look cooler than DRKs. DRKs use the scythe, though, which has it's own aesthetic appeal.

3. Depends on what you want to be doing when you party. It's pretty straightforward, white mages heal, black mages and summoners cast attack spells, warriors and paladins take damage, and the specialty fighting classes deal damage. Check out the links Mullet posted to get more info on the classes.