You are ready. You don't read math book like you read a novel. You can literally spend days on one page. You are not going to find a better book than Halmos's book; so you might as well grab a ton of scratch paper and go to town.
I do recommend that you get acquainted with the fundamentals of logic and boolean algebra first. You must become comfortable with implies, if and only if, for all, there exists, and, and or.
Since you have found your way into Stack Exchange, then you have access to quality help when your brain starts melting due to overload.
In terms of set theory, the phrase 'nothing contains everything' out of context, can implybe taken to mean either that the empty set contains all sets or that there is no such thing as the set of everything.
The first interpretation is ridiculous. The second is actually quite profound and has not always been believed.
Finally, there is something an old boss of mine once told me. "Nobody ever accomplished anything by reading the whole book." There is much in Halmos that you probably just don't need to know. Don't feel obliged to learn everything in the book.