First and foremost, relax! If you're starting classes in the fall, it's far too early to be sweating this stuff right now. Enjoy your break. Visit friends and family. Just relax.
Law school is hard but, let's face it, it's not rocket science. I think people make far too much out of the perceived intellectual intensity of law school. At the end of the day, it's all about reading and thinking about what you've read. Once you've mined the legal rule out of a particular case (or series of cases), you'll need to know the rule(s) for the exam where you will be asked to apply the rule(s) in a unique (and somewhat puzzling) issue-spotter exam question.
Here's my advice. Most certainly stay current with your class readings. As for class notes, there's no one-size-fits-all model. Every class and professor is different. Because most 1L courses utilize a heavy dose of Socratic method, you may not want to write down every utterance by your professor and classmates. More often than not (especially for the first few weeks of class), your classmates are wrong, or at best, only partially right. Thus rather than passively filling your computer with copious notes, you want to be actively listening and thinking through both the professors questions and the students answers. This is your first opportunity to attempt "thinking like a lawyer."
Where most 1Ls go wrong in the first few weeks of class (or, for some, months), in my opinion, is they harbor the belief that the professor is going to teach them the law. No, no, no. You, my friend, will teach yourself the law. This notion evades some students longer than others. They leave each class with random notes and more confused than ever. Some will even become angry at the professor for not being a better teacher. What they fail to understand is that the function of class is not to teach you law but merely demonstrate how you may or may not apply the rule(s) to particular factual situations. The same rule(s) you should have distilled from your assigned readings for class.
As for briefing cases, all you need to know is you should do it. I believe most schools cover this topic in student orientation. However, even if it is discussed in orientation, the required format still may change from professor to professor. If your professors don't specify what they want, you'll want to development something that works insofar as it allows you to answer any questions your professor may ask during class--as well as possible inclusion into your final outline.