The mindset necessary for proofs is very different from how most people learn mathematics. So long as you can get a small preview of that mindset, you'll be ahead of the game. I'd suggest choosing a source which seems "too easy", or a curriculum which is "too short". It will be enough.

Additionally, as when learning anything mathematical, don't expect too much help from Wikipedia. Pedagogy often involves telling small lies to students at first, then clearing them up later. Wikipedia has a bias towards being correct, which means that the articles can't tell those small lies and the explanations are difficult for non-experts to understand.

Congratulations on graduating high school. That's quite exciting, and I'm sure you'll love university.

The about page states that the book is for "an intermediate level (i.e., after an introductory formal logic course)." It'd be advisable to look elsewhere first if you don't have any exposure to propositional logic. For example, the first eight chapters of MIT's Mathematics for Computer Science textbook should be sufficient: https://courses.csail.mit.edu/6.042/spring17/mcs.pdf

The standard tip for reading mathematical texts is twofold: always try to come up with a proof before reading the one supplied in the text, and never ignore the problem sets. As Pólya famously put it, mathematics is not a spectator sport.

For independent study a leaner approach might be best (the open logic textbook is meant to be remixed to form a course, so it includes a lot of material). I think Daniel Velleman's "How to Prove It" is a good textbook for learning to deal with proofs, plenty of exercises there and it has a more practical approach (it is intended for CS and math students). Volker Halbach's "The Logic Manual" is good, as is Restall's "Logic", although both are oriented to philosophy students.

EDIT: s/"How to Solve It"/"How to Prove It".