No-wires/no mess with your current projection set up: Even the Apple TV, which is in itself a great device, will require a couple more wires (power and hdmi cords). Reflector will do almost everything an Apple TV can, with NO additional wires/chords. Also, you will save money ($99USD vs. $12.99USD).
Do make sure you check out the official Reflector blog for more in-depth posts on features!
Here is an affordable way to mirror your iPad/iPhone in your classroom if you do not wish to purchase the $99 Apple TV. Reflector ($12.99, formerly known as Reflection) is a great Mac/PC app that is extremely easy to set up and use.