London - Auckland Flight - best way to book it [closed]

Hi I have extensive experience in booking European flights and I have always planned all our holidays, flights accommodations by myself. But for the first time I am going to take our family of four from London to Auckland, New Zealand, and now this is different. There are a variety of questions on the flights I am trying to figure out.

1- how to get an idea about how much a good flight costs? For four, in high season Christmas, I saw quotes ranging from 3,300-3,700£. I have no idea whether these are very high prices or not.

2- how to get an idea about legs’ room - should I stick with some airlines which are notoriously better? Or is it all about the model Of the plane and I would never know till the end?

3- Transit- there are many aspects that worry me but mostly is how to protect us from missing a leg of the flight. Are any transit airports better or notoriously worse than others? Should I keep a good amount of hours in between legs? How many hours is enough and not too many?

4- travel agencies - apart from doing the digging for me, would they offer extra support in case of delays? Would they only book me flights whose luggage is checked through?

5- websites like Expedia, kayak etc do a good job at linking different companies together. I have read other articles in this forum but I still haven’t understood whether they would offer me any guarantee-reimburse-support in terms of ‘luggage checked through’ and delays.

In summary, I am thinking of starting with a kayak website to get some ideas on classic combos-costs, select 3-4 airlines based on their reputation (which I would benefit some help with) and then ring them on specific routes and see what they say. Would you say this is a good approach? Any other suggestions? Things that have worked for you or not worked? Many thanks