To make this easier, here's a picture of a BC from the Scubaboard Gallery. The black thing on the end of the corrugated hose below left of the center of the photo is the power inflator, and that is a standard piece of a BC (comes attached/with it.)

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OT but...
Is this how people use Air-2s? Obviously from my post above I don't like them, but I'd have thought you would donate reg in your mouth and use your own Air-2, given the hose lengths and desire to control your own inflator...
I agree with the point on the 1.5mm. I dive warm and cold water and I haven't found a situation where I was uncomfortably warm in my 5mm. I'd save the $ and just go with one suit that could take me down into the low 70s/high 60s.
Also, I think the piece you're seeing on BCs is the inflator, as others have said above. That does come with the BC.
If you're doing your OW locally, why not go in and have a chat with them ahead of time. Maybe your size isn't as much of an issue as you fear. Before you assume they don't have rental gear that will fit you, ask!
I'm just about to finish OW myself, and the only equipment I own is:
- wetsuit
- mask and snorkel
- full foot fins
It's kinda nice to have your own mask, because you always know it will fit. A wetsuit is worth owning, and will be useful for other water activities if you abandon diving.
I happened to own the fins for snorkelling, but I reckon I could have completed trainging perfectly happily with school fins.
There is absolutely no way I am spending money on a BCD until I have OW and I've done 20 or 30 dives - definitely a few adventure dives too. I just won't know what sort of diving I enjoy and what kind of BCD I want until then. And I recommend you take the same approach.
When I do come to buy my own gear, I'm trying it out in the pool before handing over a penny.
I talked with the die shop i will get my ow cert. with. HE said due to my size he doubts they will have a wet suit. HE also said a bc will properly be a issue. Not really a big deal because i intended to buy the stuff any way. I gave him my measurements and he told me he would check on price and what he can get in my size.
What i am thinking is atleaste my wetsuit fins mask and properly the bcd. I would perfer to wait but like he said it is doubtful most rental shops will not have my size in a bcd. No big deal. Just means alittle more money.
Being a big fellow, a custom made wetsuit is in order. For warm water diving, a 5mm suit will be fine and if you find yourself too warm you can always let a little water in to cool you down. However, if you get a 3mmm suit and get cold, well then you are just cold and not too happy.
As for a BC, a man of your size should get a backplate and wing setup. This system will fit - period. Jacket BCs will not work well for a guy your size. Trust me on that. Call Deep Sea Supply (first choice) or other company and get one BEFORE you go. If your BC does not fit properly, you will have wasted your whole trip.
The 3mm is the same price as the 1.5 kinda odd since it is twice as much rubber.
But i will not be diving when the water temp is below say 60 or so. so i think a 3mm will work i hope or i will buy a thicker one later. He also said as most of you did a 1.5 is just for protection from say jelly fish or coral.
On the other hand, your instructor may give you some comment like "what are you doing here in tech diving gear?"