Congrats on starting! I'm technically about to be a first-year PhD student, but I'll be in the UK, which splits up the Master's a PhD portions of the US combined MS/PhD. Meaning I'm actually in my third year of a PhD program. :) The number one thing I'd say is: If there's something you think is important to understand, sign up for a class in it your FIRST semester. You won't be a super productive researcher then, so it's your best shot at understanding all that really hard stuff you're dreading. I put off filling serious gaps in my math background -- gaps I knew I'd have to tackle eventually -- until my second year, and I really regretted it! I got to learn WAY cooler stuff once I had that extra background. Your first year is for filling in gaps and exploring. :)