I am not an 0L and I did well my first year of law school. One class I read some stuff over the summer, the rest I did not, so I can comment from both perspectives.
Reading over the summer was a waste of time, but was not particularly detrimental because I didn't take it very seriously. Had I intensely read or expected to have gained an advantage from reading over the summer I would have been (a) sorely disappointed and (b) a lot worse off for the effort.
Law school is a marathon, not a sprint. By the end of my second semester, I felt a bit further behind and more stressed because I had put disproportionately more effort into my first semester from the beginning (more than I should have). I would have been much better off pacing myself in the beginning of the semesters and increasing the intensity slowly as the semesters progressed, rather than coming out full throttle.
E&E's and other supplements are most helpful to when you read them along side or after you have tackled the material assigned by your professor. As a field, Torts is Torts and Contracts is Contracts. This is not true as a course, though. Prof. A's Torts will not be the same as Prof. B's Torts. Reading the supplements helps shape your understanding of the professor's take on the field. That understanding is what is going to help you excel in classes. It is much better for exams to look at the supplements through the lens of your professor's take on the class than it is to look at the professor's class through the lens of the supplement.
The burn out issue is also a serious concern. It's easy to disregard this as an 0L. It is also tempting to think that if you start sooner, you'll decrease burn out, but that is not how it usually happens. Starting earlier starts the fatigue process sooner. It's not how hard you are working, it is how long you are thinking about the topics. I also saw a lot of people who started reading over the summer get lulled into a false sense of security because of it. They got a rudimentary understanding of some of the concepts, which caused them to skim more during the actual class (which is very tempting to do because of the general work flow). As a result, they missed a lot of the pieces to the puzzle that people who were reading the material fresh picked up on.
Another thing to mention is that some supplements are likely to steer you completely wrong on some issues. All of them are out of date to some extent. CivPro and ConLaw have both had some major shake-ups in some areas in the last 2 years (and some that have come in the last few months). Reading some of these supplements can give you a wrong impression of where the law is going. (Class actions and burdens of proof/pleadings have had some serious revisions recently; sentencing and some evidentiary issues in Crim are very much in flux; equal protection in ConLaw may see some major changes in the next month; etc.)
If you really want to read, I would pick up a horn book (rather than an E&E type book) and read a chapter out of each topic (at most), not to learn any substance of the law, but rather to look at the vocabulary. Read it to pick out some of the terms of art. Wikipedia them. Get comfortable with the writing, not not learn the law. Realize, though, that you will be saving yourself, at most, a week or two of "advantage" and you could loose more than you gain by feeling more fatigued at the end of the semester when it counts.
As for once you hit class, here are some thoughts.
If your text has a case briefs supplement keyed to it, consider getting it, at least for one class (preferably something like ConLaw or CivPro, where the cases are more involved). Read the case brief first and then read the case in your book. Change it up and read the case first and then the case brief. Listen in class to see what your professor pulls out of the cases. This is a quick way to teach yourself how to pull the relevant material out of cases.
To brief or not to brief: This is an individualized thing. I book briefed my first semester (highlighter method) for a couple of weeks. After that I stopped. I found briefing to be waste of time. What I did do, and continued to do throughout, was to underline (in pen, not highlighter) and write profusely in margins. Then I made a running list of all the cases and put in a couple sentences about the case (along the lines of "Guy runs over woman several times with car, no need to prove premeditation in PA, intentional murder is enough for 1st degree"). Involved cases might get a couple of paragraphs if there was a lot of nuance and multiple dissents and/or concurrences, but I would usually write those after class to pull out just the issue that were discussed. I was able to answer questions about facts and such on call from my case book because I had written enough in the margins.
I'm a big believer in actually reading the cases rather than relying on supplements. I know other people work better the other way, though. I am not someone who can cram. My reading takes me more time than a lot of people take, but when I read I really synthesize the material. I constantly make connections between what I'm reading currently and what I've read in the past and what the professor has talked about. My margin notes often reflect that. Because of this, I think I have an easier time at the end of the semester than a lot of people. I also know that I pick up points on exams for being able to bring in details that were covered in readings, but not class or supplements.
Outlines: don't get thrown by people who make amazingly comprehensive class outlines. These are great resources for people taking that professor's class in future terms, but are of pretty limited use for exams. The best exam outlines don't outline the class, they outline exam approaches. The course is usually broken out into discrete topic areas. Exams are generally complicated hypos that touch upon many/most of those topics in one scenario. When making an outline, you should first read a bunch of practice exams to get a sense of the types of questions you will be asked. Take the various topics that were discussed in class and put them into the appropriate order for answering a question, not the appropriate order for regurgitating the class. This is often the difference between distinctions between grades.
If a particular style of studying worked for you in UG, don't reinvent the wheel. Like I said, I'm not a crammer. Lots of people are and walk around the last few weeks of the semester memorizing cases names, etc. It's easy to get thrown by that sort of thing if it isn't your style. It's generally better to go with what has been proven to work for you in the past. I synthesize as I go along and generally make sparse outlines and spend more of my time doing practice exams (sometimes writing them out fully, sometimes just outlining answers, sometimes just thinking about how I would answer the question). It works for me. It might not work for other people. That is fine.
Work on your writing. If your professor doesn't understand your answer, then you don't get credit for all of your arguments. When you get your lexis and westlaw pins, download some appellate briefs and read them (you might want to stick to SCOTUS cases so that there is a better chance that the issues were well briefed). This will give you an idea of what your writing style should be like. Recognize, though, that a good exam answer will incorporate both sides of the argument, not just one. So pull briefs from both sides of a case and then see how you would combine them to make a complete exam answer.
Good luck and don't burn yourself out this summer!