What's interesting about the one you have (Emerald) is that it's really the first time a random tour stop was filmed and released. All of the other DVDs were made-for-DVD events. Everything is bigger - bigger sets, bigger band/orchestra, bigger choir. And at least one more vocal soloist, in most of them.
The Helix show is great to see how it all started, and experience the original cast. A New Journey is my all-time favorite, and the only time there were 5 vocalists. Too many all-time classic songs in that one to list. The castle in background is awesome, and there's just something about an outdoor show that's cool. The Greatest Journey (a kind of "Greatest hits" compilation) has a mix of songs from the first two, and a documentary as bonus content. You could start with that one to get a feel for both shows in one. Songs from the Heart was a huge production, too - different castle. The only DVD with Lynn and Alex as part of the cast. Lots of classics in that show as well. Believe was the first one filmed in the US, and doesn't have quite as much of a traditional celtic feel - more pop songs. Although that was the first appearance of Teir Abhaile Riu, only without the "Singing Fight." And of course, it has our L'il Lambe singing "A Spaceman Came Traveling."
So after all that, I have no idea which one you should get first
but you really can't go wrong with any of them. I also like James' idea of going in chronological order.