1. Get an 8" screen instead of 7", if you have the room. That helps with the size issue.
2. The DVD player is a video screen. As you saw, Video and VGA are two completely different things with VGA being much higher quality.
3. A 300mhz computer won't be powerful enough to do the things you listed. MP3's, okay. Voice recognition, while playing MP3's, while doing Nav, no.
But go ahead and do the install with the system you have. You can always upgrade later and the basic stuff like the screen and power supply don't necessarily have to change.