I did not emphasize one important difference between the three options, namely, what other apps can be projected as part of the setup.
Option 1: Projector can display any AirPlay-enabled app. Right now, the number of such appls is modest, but it is expected to increase. In summary, this option will display (some) of what you are able to run on your iPad.
Option 2: Anything that your classroom PC is able to display -- you are not limited by iPad's features. This means you can project Java, Flash, Shockwave, etc.
Option 3: same as option 2.
