Kia Ora fellow kiwi.
I'd recommend Fire Red or Leaf Green first. Since they're remakes of the original games you can get a really good feel for the series. Then you can continue with the 2nd gen remakes, Heart Gold or Soul Silver, all the way up until you reach Black 2 & White 2.
As for other games, have you tried the Fire Emblem series? Its a turn-based strategy game, with great character development and story. Be careful though, the games are fairly challenging and unforgiving when a character dies.