What speed hard drive and data connection do I need to play video files?

Depending on the size of video file you are trying to play the hard disk speed you require will vary.
A good rule of thumb is the faster the better. 

If you are buying an external drive, one with a speed of 7200RPM (or greater) and a firewire connection is recommended.
USB 2.0 may provide the speed you require but there are deficiencies in the sustained data throughput of the USB protocol that can affect performance.