If you are on a modest income — under $80,000 or $120,000 for a couple — further help is available from Housing New Zealand in the form of the KiwiSaver HomeStart grant.
Once you have been making regular contributions for at least three years you may be eligible. You could get $1000 a year up to $5000, or $2000 a year up to $10,000 for a new build.
There are a few strings attached to the HomeStart grant including, as you point out, a price cap.
Those have also been tweaked and here's what Housing New Zealand had to say: "The house price cap for qualifying for the Kiwisaver deposit subsidy in Hamilton was $350,000.
"However, when KiwiSaver HomeStart launched on April 1, 2015, the house price cap for Hamilton City (as defined by the local territorial authority boundary) increased to $450,000.
"Therefore, a new build property in the city costing $400,000 will be eligible for the larger subsidy amount of between $6000 and $10,000 depending on the period of time you have contributed towards KiwiSaver at the required minimum percentage of your income.
"To qualify for a $10,000 grant you need to have been contributing to KiwiSaver for at least five years at the minimum percentage of your income.
"However, if you have been contributing for a minimum of three years or for at least four years, the grant could be either $6000 or $8000," says Housing New Zealand.
A quick search of real estate listings in Hamilton showed there were 291 homes across the city with a sticker price under $400,000, mostly three-bedroom properties.
As you say, there are also new builds available at that price point.
Other changes that came into effect in April included opening up KiwiSaver money for a deposit on a property bought off the plans.
This may also help you get into a brand new home.