I just had a look at Interactive Brokers as many/most here using it, but at first glance I think that's not suitable for me: I'd first ask them whether NZ residents can be their clients, but neither on the main page nor on the main menu or the links at the bottom I could find a "contact" link, only info/links about their advantages re trading.

I don't need a super-automated discount broker, I need a broker with real humans I can easily contact and who will reply quickly (for example to that question about NZ residents as clients), as I am used to from Schwab since many years.

In what countries can you NOT have an account with Interactive Brokers? New Zealand certainly is in the list of countries where IBKR offers accounts: interactivebrokers.com - Open account country list

Interactive Brokers is indeed a 'super-automated discount broker', but I have not usually had much trouble getting in touch with someone, by phone or by chat, on the few occasions where I needed to. The big advantages of IBKR, as far as I am concerned, are not the fact that they provide cheap trades (which they do), but that they save you money on other aspects of your investing activity:
-forex with low slippage - for instance, if you ever convert Euros to USD or get USD dividends in a European or Canadian account, you don't get the outrageous foreign exchange rates (often as much as 1% off the true exchange rate) as with most brokers
-low interest rates charged on loans, if you have any margin at all, typically LIBOR +1% or so, often several percentage points better than the competing brokers I have available to me in Canada
-high interest rates (typically something like LIBOR minus 0.5%) on positive balances beyond a benchmark of about $10,000, as opposed are not zero or close to zero interest with many brokers
-opportunity to purchase securities in not just 1-2 countries, like many brokers, but rather in dozens of countries
-accounts with stocks and cash in multiple currencies - no need to trade forex back and forth every time you buy or sell something
-rebate of half of borrow fees on shares lent out for short sale
-cheap trades (typically about $1 a trade)*

The last advantage was never the most important one, and it is particularly unimportant nowadays, when much of the competition offers the appearance of free trades. In fact, they are often making it up, and way more, by ripping you off in some other way, like providing you with a suboptimal price (payment for order flow being the big one, where they sell their clients’ orders to market makers), but also with suboptimal interest rates and suboptimal forex exchange rates. IB's philosophy is to pass along real costs to clients, plus a small profit margin, on things like share transactions, market data, loans, etc.), instead of loss-leading zero charge on share transactions but with hidden costs that often end up costing you an order of magnitude more.

I am very fond of this 'cost-plus' model, both as a client and as an investor, since I think it makes for good long-term relationships with clients. I still kick myself for not buying Costco 20 years ago (because it cost 30x earnings; the shares are up 20x since then), and I like this feature in other investments that have a similar philosophy. I'm thinking of Carmax, in car dealerships, where they basically target a $2000 margin which covers all their costs and a small profit, dand don't try to take advantage of you in a million other small ways.) I would be very interested in hearing suggestions about other examples of this kind of business strategy...

Regards DTB (full disclosure - IBKR is my third biggest holding, at 7%)

*In many countries, to compete with zero-commission brokers, IBKR also (somewhat reluctantly, I think) offers something they call IB Lite, with zero commissions but with other charges more typical of the industry. However, they apparently don't offer that option in NZ.