I bought my first one from hobby lobby. Not the cheapest one they had but the more solid brass one they sold. Since then I've tried other kinds and none have been as good as my first so I continue to use it.
Not everyone likes it. A friend of mine borrowed it and she prefers the pistol grip ones.
So it's also a matter of finding a good fit.
Another thing is that you might be pressing too hard. I see people with this issue more often then not pressing hard enough. You aren't cutting the glass. You are scoring it. If it's breaking while you are scoring, you are pressing too hard.
Also. If there are chips of glass between the glass sheet and your table , this makes the glass sheet uneven. It's more likely to break when scoring. I have a little broom/brush I use to make sure the surface I put the glass on is kept clean.
A last point I want to make is about the glass itself. Some glass cuts very easy. Like waterglass and smooth transparents. Other glass is notorious for breaking into chunks and being difficult to score properly. Like mottled glass. Mottled glass is the worst. It's super beautiful. But hard to work with.
So it could be one of the other issues I list and not necessarily the glass cutter. Or at least not just the glass cutter. But the cutter you link is not great for the fine work you are trying to do.
You also need "running pliers" if you don't have a pair.
This is the cutter I like and use. Has bad ratings though. Maybe people weren't adding oil to it? 🤷♀️
The comment about it leaking is true but they all leak. Oil will leak out of the wheel area.
The other two ratings are 5 stars.
Here is a pic of mottled glass.
Here is an Amazon kit with better cutter and the two pliers you will need.