I normally stay out of these discussions but I'm laid up with a bum leg today and so I'm bored. I'm a PADI instructor with 25 years of experience and over 3000 mostly cold water dives. I've owned and worn out multiple BCD's, owned probably 20 different regulators (they were practically given to me as an instructor and at one point, when I was doing technical diving I needed a lot), worn out one wetsuit and a half dozen drysuits. My first reaction is to say don't even consider buying much beyond mask, fins, booties and gloves before you're certified. First, you may find out you don't like or cannot dive. Secondly, no amount of reading can substitute for even a few hours underwater. Wearing the equipment in the water is very different than reading specs or even trying it on on land. Third, if you do go on to do technical diving your instructor or the particular environment or the agency may have specific gear requirements.
I cannot speak to the reason that the SSI shop will not allow you to use your own equipment in the open water class but there are many valid reasons, some of which are mentioned by davehicks and MtnDiverColorado. The shops that I've instructed for have allowed open water students to use their own gear with instructor approval. I personally would not accept your rig in a class. There are skills you will have to learn that are difficult enough with standard gear and become even more difficult with the gear you describe. It also makes it more difficult for your fellow students because the instructor has to take extra time for you. Your seven foot hose also means that your buddy will have a nonstandard experience learning alternate air exercises.
The basis of entry level scuba instruction is to teach you what you need to know to dive safely in conditions as good or better than what you trained in. It has been described as a learners permit. Once you have this cert you can go out, with a buddy, get experience and practice what you have learned. There is no substitute for time in the water. I don't teach extended range diving and the only the overhead environment teaching I do is the PADI wreck diver class but I would not even consider a student for a technical class with less than 100 dives and even then they would have to be an exceptional diver. I've run across one or two of those since I've been teaching. You are getting ahead of yourself by planning on buying a specific set of gear before you've even been in the water.
I did just work with a student who purchased all of his gear online before his open water class. He wrote a very nice review on the shop web page and he was honest enough to say that it was a mistake to purchase before he dove. I know he's already purchased a new computer and I think he is planning on buying a drysuit to replace the wetsuit he purchased before experiencing our 46 degree water.
The one advantage our students have is that the local shops all provide tanks, weights, BCD's, and exposure suits for open water. Oh, rhwestfall is absolutely right about the damage done by the pool to the gear. I insist on using shop BCD's in the pool and my drysuit booties lasted about a year when I was teaching regularly.
I wish you well and hope that diving is everything you imagine it to be. However, I really advise against purchasing gear, especially BCD's and regulators, before you've even been in the water. If you are going to go on to do technical diving then, after you are certified, find your technical instructor and get their advice on gear.
