You want to have a sharp knife with a sharp angle.
For example, I found this image on Aliexpress but don't know about this particular store. The left blade is more stable than the right one, in my experience, but is also more difficult to find.
As you can see, the blades can be replaced. This should be done rather often. Especially for fine details you need a sharp blade.
Don't use a stanley knife or standard hobby knife like here:
You need the sharper angle of the first picture to cut sharp turns.
I personally use a much smaller blade (though with the same angle), because I have found that the big blades bend too much under pressure and therefore break earlier. Also, with a smaller blade, your hand is more close to the paper, which I find comfortable.
It's a bit difficult to see because of the shadow, but it has a normal end (like the right one on the first picture). We don't need the extra stability on such a small blade.
My knife is the SDI0491. I got it as a present, so I don't know where it was bought, but if you search for the serial number you can find it. This website seems to be the producer's page.
My snap blades are called BD-100 NT Cutter Spare Blades and you can find them here (unfortunately, I can't find any other page than shops).
The knife I'm using (last picture) is sometimes called a D type cutter. You can find a product overview of some producer here (I haven't tried these knifes, but they look similar). It seems characteristic to D type to have a smaller blade.
You should have, like on the first and third pictures above, a haft with a rough surface around the place where you hold it, for better grip.
I prefer a plastic haft over a metal haft because I have the impression that with metal hafts your hand can get a bit sweaty.