Need help regarding FICO score and private loan interest rates

I'm in a bit of a difficult situation here and was wondering if anyone could offer advice or answer my questions.

I got into a top 14 law school, but will need to take out private loans to afford COL and a small portion of tuition. The problem is I won't have a FICO score until the beginning of September at the earliest and school starts in August (got a secured Mastercard in early February and it takes 6 months). In case some of you guys are not aware, they set a new federal loan limit for $50k a year in loans for law school, but top law schools typically cost closer to $100k+ a year (I got a decent scholarship, but I'm still above the limit and need to take out private loans). My parents have agreed to cosign for a private loan paying off the amount due beyond the $50k in federal loans when school begins for like $2k in tuition and the first two months of cost of living, but for the rest of it I need to take out my own private loans to afford COL once I get my FICO score. As far as I can tell from my research online, as long as I continue paying off my credit card balance immediately and keep my utilization rate low (this won't be a problem), I should expect to debut with a FICO around 750.

Can anyone confirm this is true or false regarding my FICO score expectations, and does anyone know what interest rate I should expect when I do get my FICO and start pulling loans for cost of living assuming my score hovers around 750? (a rough range is fine since I know it varies a lot). I'm terrified at the thought of randomly debuting with a bad credit score and not being able to take out private loans or getting quoted 15% after I've already paid tuition and I'm living there since it's on the other side of the country.