I've moved your post to it's own thread where it will receive more attention.
As to your question:
There are two possibilities.
You can either use a Lightning Digital AV adapter. You'll also need an HDMI cable. Connect the adapter to the iPad, and then use the HDMI cable to connect the adapter to the TV.
After trying the somewhat-clumsy cable route, I bought an Apple TV version 3. My 10 year old dumb TV has no wifi of its own, so in addition to iPad/AirPlay display, it now also has access to YouTube, Netflix, my iTunes library, and a lot of free shows I'd otherwise need a cable subscription to watch. As I type this, my 50" plasma TV is showing a live safari drive from South Africa via YouTube (Start Your Day on Safari!).
If the $150 cost of the current Apple TV 4 puts you off, look for a 3rd gen unit on the used market. If it suits your needs, you can always upgrade later.