Arcade is fast and easy to use. However, it only supports rectangular bodies (more specifically, axis-aligned, or non-rotated rectangles) and circular bodies out of the box. If you can get away with with just those shapes, Arcade is probably the best option to start with. Note that it supports custom collision callbacks, so you can technically implement other shapes yourself.
I’m less familiar with Impact, but as far as I’ve seen, it’s similar to Arcade, but it supports slopes in tilemap collisions. I haven’t encountered a another good use case for it yet.
Matter is a full-featured physics engine. It supports practically any shape for a body, it allows you to chain bodies together and make them interact in different ways. It’s slightly slower and harder to use, especially compared to Arcade, but I’d recommend it if you need complex physics.
The examples on the Phaser website can show you how each physics system works and what it supports. I can’t check the game you linked right now, but if it only has circular bodies, you might as well go for Arcade. Otherwise, you should turn to Matter.