Just stick the Pi to the back of your TV with some self-adhesive PCB risers. No case required.
Am I the only one though that uses the Pi with a (Synology) NAS with MySQL (MariaDB) to store the Kodi data, and my NAS (NFS) for the content? you can pick up where you left off from your Pi, to your laptop, or Phone.
I know...it's like Plex in architecture.
As for the remote, CEC will let you control Kodi from your TV's remote. Or if you have seperate audio, like a soundbar or AV receiver, a harmony remote will do.
- Amazon FireTV remote (connects via Bluetooth)
- Logitech F710 (if you also run RetroPie, connects via USB)
https://retropie.org.uk/ is a great emulation system for several vintage consoles (80's-early 2000's).