I didn't take a course for the ME PE. I bought the book Principles and Practice of Mechanical Engineering, Merle C. Potter, Editor, Published by Great Lakes Press.
I self-studied this book, trying to devote one evening/week for 3 months. In total, this probably amounted to about 40 hours of going over sections of the book, working problems, refamiliarizing myself with concepts,etc.
In my state (and maybe in all others??), when you sign up for the exam, the testing service sends a confirmation and lists the breakdown of questions for the PE by subject.
There are 10 questions a.m., 10 questions p.m., and you have to answer 4 in each. Although you know from what subjects the 20 questions will come, you don't know which 10 you'll see in each session. To be more effective in my studying, I decided to make sure that I knew enough subjects to be qualified to answer 13 questions (the logic being that even if one test had 10 that I knew, I could still answer 3 in the other session). In fact, that very thing happened to me--I only found 4 problems that I was comfortable with a.m., and it took me all of the 4 hours. P.M session had 9/10 problems that I knew I could answer; I finished the 4 I needed, relaxed, doublechecked my work and left with nearly 1 1/2 hours to spare.
While I won't say that my "learn 65% well" will work for everybody, I passed the test on the first attempt, so I guess it worked for me.
Rich's comment of coffee and relaxing is a good one. Also, take LOTS of books, but be smart about it. I probably had a dozen books with me--4 general purpose books and the rest subject-specific. My intent was to use the subject-specific books only as a safety net. In the a.m. session that safety net was useful for one problem. In the p.m. session, as I found very familiar problems, I didn't crack open a single one of the "subject" books.
You're allowed as many books as you want, so don't leave any at home that you think may be useful. I saw two people bringing in books in Radio Flyer wagons. It's noteworthy that they also left early with their Radio Flyer wagons, suggesting that they were more prepared than most.
Good luck