Cheap arduino wi-fi TRIGGER
WiFi you either need a WiFi router or for either the iPhone or Arduino to create a network.

RF transceiver you need external circuitry.

The common way to do this at the moment is using Bluetooth Low Energy. Using a Bluetooth Low Energy (BLE) shield you can directly connect the Arduino to a modern iPhone or Android phone (supporting Bluetooth 4.0).

Check out redbearlabs, who have a range of shields and BLE-enabled Arduino clones. There are example sketches and iOS apps on the net. I have made a BLE controlled RGB light using the redbearlabs BlendMicro and example OSX application.