I've been researching different ACT essay "step-by-step examples" and I'm confused about which to follow.
I've read one guide that specified choosing one perspective and proving it right over the other ones, as opposed to evaluating all 3 perspectives and bringing up evidence and counter evidence for each one.
Will one of these approaches give me a better score?
Both of the strategies you mention are valid approaches to the essay. However, the most foolproof way to write a coherent essay is to use the second method (evaluating all three perspectives). The instructions for the ACT essay ask you to "write a unified, coherent essay in which you evaluate multiple perspectives" on the issue at hand. In order to earn a high score, you must address each perspective. If you stick to this structure, you'll be sure to fulfill all the expectations of the essay graders.
If you chose the perspective labeled "Perspective 3" the simplest way to structure your essay would be to devote the first body paragraph to explaining why Perspective 1 is a commonly held viewpoint and why you disagree with it. Then, use the second body paragraph to do the same for Perspective 2. Finally, in the third body paragraph, tie your counterarguments together with additional points supporting Perspective 3. Here's a sample essay that we've written on our blog that follows this methodology so you can see how the writing process develops.