Start with the honest part: this is a long way, so give it the time
Fifteen hours or more in the air, and you cross the date line on the way. You leave on a Monday and land on a Wednesday, then get that day back coming home. It confuses everyone the first time.
Two weeks is the working minimum and three is better. A ten-day trip to Australia spends a quarter of itself in transit, and people come home saying they saw the inside of airports. If two weeks is genuinely all you have, do one country properly rather than three badly.
Breaking the flight in Fiji is the move most people do not think of. A few nights on the way over or back turns the hardest part of the trip into part of the trip. It costs less than people assume and it changes how you arrive.
Seasons are upside down
Their summer runs December through February, which is when Americans most want to go and when prices and crowds are at their highest.
New Zealand. October to November and March to April are the sweet spots. Fewer people, prices come down, and the scenery does not care what month it is.
Australia. Depends entirely on which Australia. Sydney and Melbourne are pleasant most of the year. The Great Barrier Reef and the tropical north are at their best roughly May through October, which is the dry season. That window also sits outside the stinger season, when swimming in northern Queensland means a suit or a netted enclosure.
Fiji. May through October is dry season and the reliable choice.
New Zealand: which island, and why not both
The South Island is the one in the photographs. Mountains, fiords, glaciers, the drives people describe for years afterward. The North Island is where the Maori culture, the geothermal areas and most of the cities are.
Most first-timers want both, and two weeks will do it if you are disciplined. What does not work is treating the map like a European one. The distances are longer than they look, the roads are two lanes and beautiful rather than fast, and you will want to stop constantly. Budget the driving generously and you will love it. Budget it tightly and you will spend the trip behind the wheel.
You drive on the left, which most people adapt to within a day. Roundabouts and turning across traffic are where the concentration goes.
Australia is three flights, not one trip
Sydney, the Reef and Uluru are the classic three, and they are separated by domestic flights of several hours each. That is normal here and it needs building into the plan rather than discovering.
If you only have room for two, Sydney plus the Reef is the easier, more comfortable pairing. Uluru is the one people are most moved by and the one that asks the most of you, and it deserves proper time rather than a stopover.
Worth knowing before you book
Both Australia and New Zealand require travel authorization in advance for American visitors. They are straightforward online applications, and they are not the sort of thing to leave to the week before.
The Reef is a booking, not a place you turn up at. Which operator, which part of the reef, and how far out they go make an enormous difference to what you actually see, and the good ones fill up.
Bring layers everywhere. New Zealand in particular can deliver four seasons in an afternoon, and the sun there is genuinely stronger than what you are used to.