Definitely a Raspberry Pi.
You can buy it in Korea from these guys (ask your co-T for help to order, but you don't need an account, just make an order and send them some money via the ATM).http://eleparts.co.kr/EPXGNNFFbrand
It looks like that set includes the Pi 3, case, heatsink, power supply. The heatsink is a bit of a gimmick and not really necessary. The case is nice, but there are others. The PSU is ok, but any good quality 2.5A or better phone charger will work.
You might already have everything else. Here's what you need to make it go.
Micro SD card
Monitor with HDMI input
Speakers (or use speakers on HDMI monitor)
Then download and install one of the Kodi distributions. Most recently I heard that LibreElec was best, but there are others.
You can write the Kodi files to the SD card on a Windows PC (you'll need some kind of Micro SD card reader). Then once the Pi is on your network you can use some software on your smartphone to control it (so you won't need the keyboard and mouse anymore).