Welcome! Here's what I suggest:
1: I would take some time to research the schools you are going to apply to as they usually have a date by which the GMAT ought to be taken. That should help you establish the amount of study time you have. I would also suggest NOT leaving room to take it again. Leaving yourself time to take it a second time is only a psychological game you are playing with yourself that will only hurt your score/ego. For instance, should you leave time to take it a second time you would have to decide how much time in between the two tests you would like to allow yourself. If you were me in this situation, I would take the first GMAT sooner so as to give myself plenty of time to study and prepare for the second if necessary. However, it seems fairly obvious that I will not perform to my potential on the first test for two reasons. The first being the obvious fact that I have had less time to prepare. The second being that while I was studying I wasn't taking it as serious because I knew that I could still retake it, so naturally I wasn't studying as hard. SO, when you get your dissatisfying first results back you PANIC because you've got this "horrible" score that schools will see on your record regardless of how well you do the second time (some schools even average scores of all the tests you take....EEEEEEK!) and now you THINK that you can't do very much better. Also, you essentially wasted all that time you spent ineffectively studying for the first test.
I would recommend only setting one date and I would set it probably a week before the deadline in case something sudden comes up right before the test that would cause you too have to reschedule the date. Having firmly in your mind the concept that you do indeed only get one shot to nail this thing will give you the proper motivation to use your time wisely between now and test date.
2: Before you even get to the books I would take a diagnostic test. Try the free GMATPrep tests
found on mba.com. Taking one of these will give you an idea of where your strengths and weaknesses are and will aid you in finding the perfect book that will address these needs. When you do take this test, DO NOT PANIC if your score is a 500 or less and you are aiming to get 750+ (lower score means there's so much more room for quantifiable improvement). It's good to know that now when there is plenty of time to bring that score up. On a similar note, if you score something you're satisfied with I would still spend a considerable amount of time studying/preparing and perhaps taking another practice test to confirm such a result. Once you find out where you stand, I would buy a prep book that goes over the concepts that are specifically tested on the GMAT. If you find that your math skills are a bit weak as you suggest, definitely read a book that goes into both the basics and more advanced topics. Personally, I only used Barron's and OG11
to do my studying. The OG book is the closest thing you'll get to actual GMAT questions, so I would honestly leave this book as the last thing you use to study. For example, if you do struggle with math, go through Barron's or Princeton or one of the others (I've heard good things about all of them) and once you feel you have mastered the concepts tested (or at least have become satisfied with your knowledge level of these concepts) I would turn to OG. By this time the new version may or may not be out so I would just pick up the latest one available, however, if you are ready to start the OG before the new one comes out, get the old one. I don't think that the test is going through any major changes that would warrant the use of the newer edition (they may even share many of the same questions).
3: The best way of studying is NOT taking practice test over and over again. The best way is to take a practice test and know precisely the methodology of answering every question on the test, even the ones you get correct. Take a couple practice tests yes, but definitely review the answers and know why each answer is correct/incorrect and how to arrive at such a conclusion. The GMATPrep tests
do not explain why answers are right or wrong but OG does, so with every question in the OG I would spend most of my time understanding the logic to solving each and every problem because the methods/logic will most likely appear again on the real deal while specific questions are very unlikely to do so. Even with questions you answer correctly, be sure to review the answer guide to see how to solve them because there may be a shortcut that you could've taken that would have saved you time, which for many is an issue on the test.
4: Not knowing where you stand with the test, I would still say 4 months will give you plenty of time to study. If you take the practice test, find it easy, and score in your target range then I would not get too stressed. That being said, if you fall somewhere well below your target score, 4 months should give you enough time to improve and reach your target.