Very briefly:.....
iPad 2 Wi-Fi- 16GB
This one needs to be able to access a Wi-Fi network to be connected to and use the internet. Your home internet modem / router can provide this if it has Wi-Fi as part of it's equipment. Otherwise you can use it with public WiFi hotspots where they are provided.
iPad 2 Wi-Fi + 3G 16GB
In addition to the above, this one offers the option of operating away from a fixed WiFi network using the 3G mobile phone network. To do this, it needs a 3G mobile phone card with a data "package". Coverage in this mode is limited to that offered by the cell locations of you chosen mobile phone company. NZ Telecom would seem to offer the best coverage. This model iPad's cost is greater for that reason. You also need to budget for the costs of your 3G mobile data package. It is the much more convenient option if you travel around a bit.
If either of you have a mobile phone which can be set to operate as a mobile "hot spot" this may enable you to use option one above with your phone as the internet provider / bridge, however data charges will apply to you normal mobile phone account, and you have to configure two devices when ever you want to operate away from home in this manner.
Not as brief as I had hoped, but that's how it works for me on this side of the ditch.
FOR
PS Edited to add that you need to be sure that in option two, your iPad mobile phone configuration works with the mobile phone network of your preference. Since you have mentioned 3G, I think NZT would be compatible, but confirm this with the sales people before handing over money.
Last edited by FullOppositeRudder; 18th August 2013 at 05:20.