Getting your VA benefits works very smoothly here.
In your case, if you want an accurate estimate of what will be paid for, what won't, and when, I would suggest getting your application in ASAP. After you do this, you will receive an enrollment agreement form that spells out in detail what your expected charges will be. This is your starting point.
When you receive the enrollment form, you would then contact our VA counselor. She can go over the details of timing, and how much you can expect for reimbursement and when.
Generally, however, all of your eligible expenses for that month are tallied up at the end of the month and sent in for reimbursement.
As far as how much of a loan to get, assuming you are going the KEY loan route (this is pretty much what everybody does), I would suggest waiting to get back your enrollment agreement and then applying. You will have a much better idea of your expenses then. Once you are approved (takes 2 mins. online) and the school has certified it, adjusting how much you ACTUALLY take out and when the disbursements are can be easily worked out with our financial aid counselor.
I wouldn't stress too much about the financial aspects of coming here. Assuming you have already decided to come here and to use some financing to do it, I think you will find that part to be very smooth. The VA and FINANCIAL AID ladies are both very nice and more than willing to help get your questions answered and any issues worked out.
I know my suggestions are not as specific as what you may have been looking for, but I hope it helps anyway.
FYI - you can always call FSA and ask to talk to VA or FINANCIAL AID to get more specific answers for your situation.