Good luck with your upcoming class........here is the order I would buy gear in and why..............
I have posted this before..........my list assumes that you have access to decent rental gear from a reputable dive shop and you don't intend to drop all the money at once........
Mask - key is leak free fit and comfort (current favorite is the AL Mythos)
Booties - fit, sanitary, many places don't have them has rentals, without wide soles, so they fit a wider range of fins..........
See-me tube (DSMB) & whistle - safety (my favorite is Carter 35 lb Personal float and Storm Whistle)
LED light - again safety and lots to see under rocks and crevices (current favorite is a SP Fuego)
Paramedic shears - safety
Wrist Computer - makes diving easier.....also assumes you have a decent scuba watch as a back-up time piece (I/m a big Suunto Gekko fan).
The computer before reg seems to be controversial (or even buying one at all if you are an infrequent diver).......in my opinion the computer makes diving so much easier.....you still need to fully learn/understand tables.....for me diving is all about fun and relaxation......also computers can be a bit complex, you need to know how to use it and exactly what the screens mean, I think computers as rentals are not the best idea.......so computer comes first for me.......
Above is my minimum kit.........easy to pack, travel with and gets me in the water with some basic typically easy to rent gear.
Fins - unless you have leg/joint/cramp issues, then fins become more important and bump up to my must have list, make sure you have your booties with you when you buy them, fit is critical (for most recreational reef diving SP Twin Jets, yellow, but I also have Lighting Jet paddle fins with SS straps).
Wetsuit - all about fit and comfort, suitable for the waters temps in which you do most of your diving, a good 3-mil jumpsuit as an all-rounder, you can add a hooded vest and gloves for cooler water.....(Henderson Hyperstretch all the way)
I would stop here unless you plan to dive a lot...........
Regulator and BC (or BP/W) - purchase them together as a set, that way all the hoses can be the correct length and if you choose to go with a inflator mounted second stage (Air II, etc) you have that option.
Gauges, just a simple small brass and glass pressure gauge.....
Remember regs and BC require annual maintenance......
Finally tanks............remember they need annual inspections and 5-year hydros......
Other items to consider.............
Compass - underwater navigation if that it the type of diving you do
Second light - if you do lots of night diving
Second computer - nice to have a backup, I almost always dive with two
Finger spool - so you can launch your DSMB from underwater
My final thought is.......used gear.......you can find some great deals, I now buy most of my gear as used........
Hope this helps........M