I agree with @Gerben - the nRF24L01+ would probably be the most suitable for your application. It should have enough range to go 15m through a few walls, and the cost is about as cheap as you can get.
You can pick up cheap Chinese clone modules (not real nRF24L01+ but another chip that operates exactly the same) for around $2 each on eBay. I by them by the bag full.
There are a few good libraries around for controlling them with an Arduino so programming really isn't much of a problem.
They even have the advantage that they can operate in a mesh network mode if you ever expand your system to incorporate other things.
The connection to the module is a simple 5-wire SPI interface - SDC, MOSI, MISO, Chip Enable and Command Select pins, so you don't even need to mess with lots of wires.
You can read more about using them here: http://playground.arduino.cc/InterfacingWithHardware/Nrf24L01
The best library in existence is the RF24Network library: https://github.com/maniacbug/RF24Network
If you are looking for something more self-contained and stand-alone, you might look at the ESP8266 modules which are a programmable WiFi module. They can either interface with an Arduino to be controlled through AT commands, which is quite nasty, or they can be programmed directly using an Arduino-like API which can be obtained here: https://github.com/esp8266/Arduino
These modules are a little more expensive, but that cost is offset by not then needing an Arduino in the mix as well. The NodeMCU is probably the easiest to work with since it contains the USB serial interface on board like an Arduino. It also has its own Lua based programming environment if you don't mind learning another new language, but you can use it with the Arduino API for ESP8266 above.
The ESP8266 is also supported by the beta version of UECIDE