Getting a DVI female to male HDMI coupler may be cheaper than a special DVI to HDMI cable. I use this method on my Sony TV with no issue. Then as Surf mentioned just get coax or Toslink cable for audio, or even RCA if stereo is all you need.
As for the DVD player, do you need to select Progressive Scan (480p VIA cOMP cables because if you do then the signal may default to standard 480I signal and not look great.
For a new player you cant go wrong with any Oppo unit and they are under $200 for most models, these players have tested better than about any picture out there regardless of price.........just make sure the model states it will "upconvert".