Of course there is cost to setting up student accounts and, depending on your school's policies, running a server.  One way to get your feet wet and see if Minecraft is a good fit for your curriculum is to use the classic version for a lesson or two first.

There are some pretty significant changes between the Classic version (0.30) and the current version (1.6.6), but the look and feel of both versions is quite similar.

Positive diferences:

• 100% Free - If you already have computers and an internet connection, nothing needs to be paid to get you started. 
• Infinite blocks - Assuming the students are required to build something for your assignment, they have no need to harvest materials.  They can simply find a good location and get started with construction.
• No account needed - The classic version is fully COPA compliant and can be used with younger students without a need for permission slips. 
• "Cheat Codes" - These aren't really cheating as they're listed on the same page as the classic version itself, but there are certain key commands that can make the game much easier.  For example, a student who has become lost or dug down into lava can press "r" to return to their original spawn point.
• No deaths - There are no hearts in the classic version.  Students can fall impossible distances, stay underwater indefinitely, and even take a swim through lava without damaging their character.

Negative differences:

• No crafting - While many blocks are in infinite supply, other blocks (and almost all other items) are not available.   There are no ladders, maps, doors, and so on.
• No saved games - Unless you have created accounts for your students or are hosting a server, whatever world they've created will cease to exist once they leave the website.
• Not 100% Mac Compatible - Java for Mac OS X is not quite the same as Java for Windows.  Issues can range from the cursor remaining on the screen when playing to the game not loading at all.  (That last glitch seems to be limited to computers that also have the full client installed.)