Make sure everybody owns a a Nintendo DS, then load up Pictochat.

Retroarch box for your TV?

You can buy a USB blu-ray drive for like $50.

Rather than build a computer, check out NAS devices.

My Synology NAS does everything you mention except ripping, and you can rip with any computer that has an optional drive.

A NAS is lower power than a tower server, and many are designed to let you swap hard drives.