How much work do you want to do?
None - Librelec is already configured for media center usage. Install and use.
Little - Fedora IOT. Set up the system, which has a small core, verify you've got the right drivers, plasma bigscreen, your media apps.
Lots - Arch linux. Same thing, set up the small core (manually), then handle drivers, plasma bigscreen, your media apps.
Lots (But I don't like systemd). Go Void. It's the same as arch (more or less) but you use runit instead of systemd.
Full Control. Go Gentoo. This is probably overkill here unless you've got some kind of restrictions to meet. You know your needs best.