Here is my list.
Mask-about $30 from Dive Gear Express
Fins-about $100. I prefer either Dive Rite XT, or the Deep6 fins. Add in booties of some sort, I prefer NRS kayaking boots to any dive boot I've tried
Snorkel-find one to borrow, you don't really need one, but Piranha has some cheap folding snorkels. You're scuba diving not snorkeling, buy a cheap one and take it off of your mask when you are no longer required to wear it.
IP gauge-$20 from DGX. Whether you own or rent regulators, that is the only way you can tell if the first stage is healthy if it isn't leaking. Very important to have.
After that, my 100% unequivocal top priority if you want to dive locally is exposure protection. In Michigan that is either a really nice 7mm/semidry or more preferably a drysuit with a nice hood. It's expensive, but it is what it is. Reason for that is you can almost always find regs/bcs/tanks to borrow or rent that are good enough but finding high quality exposure protection to rent is quite difficult. Current suit recommendation is from Othree
If you are a travelling diver only, then change that to a regulator set and computer. You can get a great computer for about $200 from Dive Gear Express with the DG03 that is truly all you need.
After you've got all of that, then get a bc of some sort. I highly recommend the Deep Sea Supply backplate and wings as I think they are the best value out there.
Tanks are last. I only recommend buying tanks in pairs, and only buying used tanks. That will be $200-$400 for a pair depending on aluminum vs. steel
So, call it $200 for Mask/Fin/Snorkel/Booties
$400 for a nice semidry wetsuit and hood from O3, or about $1500 for a drysuit with P-valve etc
I very much believe in buying a doubles set of regulators for the spare first stage. Saves a lot of grief if you have an issue. From Deep6 it's about $900, plus $200 for the computer
DSS bpw is $500.
Total cost is about $2500 for wetsuit with tanks, or about $3500 for a drysuit with tanks. That gear will last you basically forever, and if you get into any tech diving the only thing you have to buy is the double tanks and a wing. If you go to a pony bottle, you only have to get a reg hose and an extra spg. The most flexible system right there and that is the order that I recommend all students purchase gear in unless you randomly find a screaming deal on something out of order.