HDMI, most likely.... but depends on the DVD player you have.... I would've think all DVD players would have HDMI, but can't confirm that 100%.
From your phone, probably not without use of adapters. There's no video "out", so for any chance, it would need to be USB to OTG adapter, then USB to HDMI adapters....... not "easier", and definitely not guaranteed to work.
As for the monitor itself.... does it have speakers built in? Without, you'll literally only be "watching" a movie.