I would go through them all together, both to preserve your sanity and to better simulate the fact that our brain will need to be good at all three things at once.
I would probably read two chapters at a time in each book (maybe one at a time in Reading Comp, since there are fewer there).
After reading a couple chapters, you would ideally then do some actual prep test practice to reinforce the ideas and experiment with the techniques.
For example, if you were reading a chapter about Assumption Questions, you should then spend a few study sessions going through Logical Reasoning sections and trying the Assumption questions.
If you're reading about Ordering Games, go find and attempt some ordering games.
There is a Self-Study Starter Kit online ... just look right after the table of contents in your strategy guide (I'm looking at the LR one right now) ... it gives you a link to go to where you can grab a self-study syllabus (as well as some other resources).
http://www.manhattanlsat.com/access.cfmIf you don't already have access to official prep tests, you definitely want to have at least 20 or so to work from.
You might want to set aside half the tests you have for carving them up for individual question types (like what I was just describing) ... that way the other tests you have will be saved for doing complete start-to-finish practice tests.
While a syllabus would be friendly in terms of pointing you to where you can find a given question type / game type / passage type ... the act of you having to find it yourself will actually be tremendous practice when it comes to training your brain on the identifying characteristics of each type.
You'll probably find that you get a lot out of the Strategy guides on your SECOND read-through. So try not to get too bogged down with anything on your first pass. You should envision that you'll get maximal benefit by reading about something, trying a bunch of examples of it, and then later reading about it again (it makes more sense the 2nd time, with some experience under your belt).
You could probably realistically shoot for doing one chapter from each book each week (that is, complete 1 RC, 1 Games, 1 LR chapter + practice questions per week).
Good luck. Let me know if you have follow up questions.