I believe all AirNZ planes have personal inflight entertainment now; Emirates and Singapore Airlines certainly do. The extra luggage is on AirNZ via LA only. Some planes have extra legroom - check on here
http://www.cheapflights.com/travel-tips/legroom.html and you will see AirNZ rates good.
Getting the cheapest flight is difficult as the prices can change daily. At the moment you would have to pay around GBP630-730 for a cheap return economy ticket for 16 April. Booking online means looking at all the airline sites, and bucket shops like travelbag.co.uk and expedia.co.uk to get the best prices. I often have to do this for the husband visits and find the prices can change daily - once after two days of angst I was about to book a ticket through Travelbag when I found the airline itself (Singapore in this case) was doing a special that day GBP100 cheaper! I presume you have decided whether you are getting a return, or are waiting for that PR to get a one-way ticket. One site I am not that impressed about is lastminute.com - it may be that there would be a lastminute bargain but generally they are expensive.
Some airlines you can pick your seat online (can't remember which) but most you pick your seat at check-in. Unfortunately, I do not think you can choose your near neighbours! :)
It is a four hour drive from Auckland to Whakatane, 45mins on a plane. The international and domestic terminals are next to each other at Auckland and you would go through Auckland immigration and customs then to the domestic terminal (allow 2+ hours). I think there is a limit of 20kg of luggage each on domestic flights, so if you are taking double that from going via AirNZ and LA maybe renting a car and driving would be better.
I am not absolutely sure here whether they would waive newly immigrants extra luggage - I would think not as the plane to Whakatane would most probably be a small 30 seater, maybe 50 seater. Flights to Whakatane cost between $139 and $209 at the moment - you may have to book these pretty soon as you are arriving nearing the end of the school holidays and flights fill up quickly at this time.
HTH. :)