Couple of your questions I didn't answer...
You can get by just with the Battlechest for now if you want. It will give you the first 2 expansions, so you can level up to 80. You'll get access to all the Vanilla classes and races, as well as Blood Elf and Draenai races from Burning Crusade. And Deathknight Hero class from Wrath of the Lich King(You have to have a level 55 or higher of any other class to unlock Deathknights, because they start at level 55). As far as professions go, you'll get everything except Archaeology.
Adding Cataclysm will give you access to the Worgen and Goblin races. As well as Archaeology profession. And level cap of 85
And Mists of Pandaria will give you Pandas(They're cooler then they sound) and the Monk class. And level cap of 90.
Summary and rundown of the classes. Really just depends on your playstyle. With exception to the Rogue(awesome class, just not my thing), i've played them all. And they're all fun in their own way.
If you do play, just take your time and enjoy it. Smell the roses. I wish I could go back and re-experience the game for the first time again. As much as i've enjoyed it since, the magic of playing it the first time will never be the same.