I love the idea of the Raspberry Pi, but there are some cheaper alternative single board computers that offer a similar experience for a fraction of the cost. While the community support isn't quite what it is for the Pi, there are a ton of projects you can accomplish on the cheap with these little hidden gems. Keep an eye on AliExpress and Amazon and you can find SBC's sporting quad core ARM process with 2-4 GB of RAM for under $30, including a power supply and IR remote control.
The box used in this video is a Sunvell T95x I picked up refurbished on Amazon for $12.99 shipped. It sports a quad Core Amlogic S905x @ 2GHz and 1 GB of DDR3 RAM.
EmuElec is essentially the RetroPie equivalent for other single board computers, running only the bare minimum Linux core to get EmulationStation running.
Things You Will Need
Downloads and Flashing to MicroSD
Booting to EmuElec for the First Time
Special thanks to the developers of EmuElec for making this amazing software