My $0.02
Buy fins and mask now. Fit is important. Fins can be cheap as you will change.Try them on in a shop. Even though warranty is not a big issue with these, purchasing on line won't serve you.
Don't just depend on the "suck" test for the mask. Make sure it lays on your face with a nice seal without inhaling.
Do your class using their gear. Ask to change BC's etc and see what works.
Then if you know you are going to stay with the activity, buy a regs and SPG that will serve your plans. Make it a good one. Don't cheat yourself. Does not have to be the best of the best. It may be just me, but I prefer to know the history of my gas delivery system.
I would also buy over the counter from an authorized dealer for the warranty. (I have had Scubapro regs for 5 years purchased through an authorized dealer. With the free parts for life, I am pretty close to making up the Leisurepro price difference.)
Then rent and borrow as many BC's etc as possible until you know what works for you.
At some point, sooner rather than later get your own exposure protection as well.
My daughter is doing her open water now. I am buying her a Scubapro Mk11 w/ S555. Not their top of the line, but one of their better combinations. And if she does not stick with the sport it'll be a good back up for me. Part of the the reason for Scubapro, quality product. I have good experience with them. Also very important I have 3 Scubapro dealers in the area. Get a quality reg. I would recommend having somebody on hand who can take care of warranty and QC issues. I have no plans in the near future to purchase a BC until I have exhausted every loaner available to me including BP/w's.