I use Debian. If you install the kodi package, you also get the Kodi desktop environment installed.
On your login screen, you will find a menu to choose between different desktop environments. On lightdm you can open it by clicking the wrench icon in the top menubar.
There you can select Kodi and log into your system.
If you want to invest in new hardware, I would suggest getting a mini PC. You can get these refurbished for under 100€. Add a wireless keyboard with touchpad (Logitech K400 or Microsoft Media Keyboard) and install Linux+Kodi.
You can select Kodi in your login manager to start straight into Kodi, so you dont have to mess with a desktop environment if you just want to watch a movie.
KDE is also developing a desktop environment for TVs called Plasma Bigscreen, although I haven't tried this one.
And unlike devices with a locked down, proprietary OS you can run any desktop application or game on it (if the hardware supports it).