I would recommend buying the battle chest. It includes the original and Burning Crusade. That usually runs about $40. You don't have to worry about Wrath of the Lich King if you are just starting out. Its just high level stuff. As far as I know anyways, someone correct me if I'm wrong.
And you will have to buy two accounts. Like wafflehammer said you can install on as many computers as you want from the disks but you will need to buy a different account for each one.