Do you plan to buy everything you need for basic diving all at once, or spread out?
Some of the best advice I got was from my instructor. "What part of the rental gear do you hate the most, whatever it is, buy that first."
-It's always good to have a small light, even f you aren't doing night dives yet.
-A knife of some sort, doesn't have to be rambo size, just something to cut line or anything you could get snagged up in. Blunt tip will keep you from stabbing you or your gear.
-A whistle is a good safety item and cheap.
-Save a dive kit, or some spare parts and o-rings, always o-rings.
-Dive bag, but I use a tote, cheaper that way. If you plan to travel with your gear, I suggest a good bag that will protect your gear, but a dive bag is also a great target for theft in the airport. Some come with a bag that goes over it for disguise.
-Weights and weight belt, if your bc isn't weight integraded.
-Tank, size and valve type. There are a ton of sizes other than the standard al80. rent a few different sizes to see which works for you. It is all about personal preference. yoke or Din. Depends on type of diving and preference. Rec. diving within limits, I use a yoke.
-Reg. bag. Something you can use to stuff that expensive gear into.
I'm sure I'm leaving something out, but there are some of the basics.
Hope this helps you, and good luck on your advanced class.