Hi CLTpkg,
If you have 3 months to study, taking your first CAT in Week 5 shouldn't be an issue.
You should really spend the first five weeks getting all the concepts and material down. Doing Tests before this point may not yield accurate results and you waste a CAT. For example, if you come across geometry questions that you could tackle, your lack of knowledge may prohibit you from gagging your true skill level.
In your studies, I would recommend you make flash cards for all things Quant, and Sentence Correction flash cards for Verbal. This will help you keep the concepts fresh (from Weeks 5-12). During this period I think you should aim for 1 full CAT a week, and do a complete analysis of your score going question by question. Keep a Notebook or make a separate set of Flash Cards highlighting your weaknesses, so that you can improve from it.
I have been studying for the GMAT since February, and plan to give the exam this weekend. What I have mentioned is what I wish I knew from the beginning. Although I am confident in my abilities come test day, I feel I could have been much more efficient had I focused on getting the material down earlier than dedicating time to strategy and analysis when a lot of my errors were coming from knowledge gaps.
Good Luck and Happy Studying!! Believe that you can and will get the score you desire!