Minecraft is an excellent game. If we ever get server hardware set up perhaps we should set up a server and make some interesting stuff.
The difference between Classic and Alpha is that Classic is free and functions more as a sandbox for making structures or exploring, while Alpha requires a purchase, includes more features such as crafting and is more of a survival mode where balances building with fending off monsters.
It's definitely worth the $10, and y'all should buy it before it enters the next stage of production and gets more expensive.
P.S. The interface on the site isn't the best, so if you sign up, be particularly careful to enter the right email address, since you only enter it once and as of right now there appears to be no way to change it.