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Hi, I need to buy a used hatchback car with the budget around 5500-6000 $.
I am looking for a automatic and low km car (under 100,000 km) and year of 2004-2006.

I have found some makes on trademe such as Mazda demio, Mazda verisa, Suzuki swift, Toyota passo, Toyota ist, Toyota vitz, Honda jazz or fit, Nissan tida, Nissan note and .....
Since I am not familiar with these cars I need help.
I know some models have cvt which is not good for this age of cars. and also some cars have camchain which is better than cambelt.

For this budget which model is better? can I find suitable car with this budget?

The research you have already done is good, and you've identified the main area of concern for vehicles of this age and type (ie; CVT transmissions).
The Honda Jazz/Fit had a CVT transmission which (from this era) was known to give trouble, likewise, most import Nissan Tiidas had CVTs too, although NZ New examples didn't. On that basis, I'd have a preference for the Mazda and Toyota product, but again, some (but not all) Japanese imports had CVTs.
All of these cars should have chains rather than cambelts, although with Japanese domestic spec cars that sometimes have different engines to NZ market modles, it would pay to check.
As you can see, it pays to ask and check the specifics of each car you're looking at to reduce the risk.

Many thanks for your answer.
Would you pls let me know which type of Mazda and Toyota are good for this budget?

Actually I am new in new Zealand, so would you pls let me know the difference between buying car from private owners and dealers?

Thanks again for your help

It really comes down to which one suits your needs best. The Mazda Demio and Verisa are both fine from a reliability perspective and with Toyota, almost all their models have a good reputation for reliability. As I said before, ask the seller which transmission it has.
Buying from a dealer gives you more security and peace of mind as a dealer is bound by the Consumer Guarantees Act (CGA), which means that he must repair any defects for a "reasonable" time after purchase. Don't be fooled by the dealer saying the car has a 30 day warranty (or any stipulated time), as the CGA does not have any specific end date, although with a relatively low value car, the CGA will expire earlier than a high value, late model car. In reality, perhaps 3 months would seem reasonable on a car such as this.
With a private sale, there are no guarantees, so if the car fails after one day, the seller will not be responsible unless you can prove that he misrepresented the vehicle.
A dealer is obviously the safer bet.

Many Thanks for your answer.
It would appreciated if you could let me know the difference between Toyota ist, Toyota ist hid selection and Toyota ist 1.3 fl edition hid selection.

Thanks again for your help

These descriptions merely relate to spec level. For example, the HID refers to High Intensity Discharge Headlamps. Some of these models may have alloy wheels compared with steel wheels and plastic hubcaps etc.
The best advice is to find the best condition, lowest mileage example you can find, with the spec being secondary (unless there's something you particularly want).
HID headlamps for example produce a very bright white light, but can be very expensive to replace if they fail, unlike a bulb which is quite cheap. So, while you might particularly like HID lamps, to my mind I wouldn't let that be the determining factor in my purchase decision - I'd want the best kept car with or without them.