To sum up what's been said,
The basic single tank set up for a BP/W (Backplate/Wing) is the following:
Backplate (Stainless Steel, Aluminum, Synthetic)
Harness (1 piece Hogarthian, or with buckles and swivels etc)
Wing (anything under 40lbs for singles)
Cambands (tank bands, 2 required)
Optional:
STA - Single tank Adapter
Crotch Strap
Backplates are mainly made from Stainless Steel (SS - 5-6lbs) or Aluminum (Al - 1.5-3lbs). They make plastic and synthetic backplates which are near neutral. The latter usually comes as a package with it's own harness etc (see Dive Rite Transpac and Zeagle Express Tech)
Some come with slots for your cambands in which case an single tank adapter (STA) would be optional if your wing comes integrated with a "rollbar".
An STA is usually weighted to 1lb, with SS buckle cambands you now have 3 extra pounds total to the plate.
They make some STA's that can be fitted with a lead block to add more pounds to it.
STA also allow you to attach your cambands to the STA itself so if you want to take apart your set up you don't have to unlace and relace your cambands (which gets old REAL quick)
With your backplate you'll see holes drilled into them which can be used with bolts and nuts to attach pockets, clips, accessories, and anything you can imagine.
Your Bp/W and STA are all held together by SS wingnuts and bolts. Very secure.
Everything sits right on your center of gravity on your back, so horizontal trim comes naturally to you, unless of course you load a large ratio of weight on your belt or hip pockets (purchased separately).
A single piece Hogarthian Harness (Hog) is usually the cheapest route and when fitted right can be taken off just as quick if not quicker than any other BC (less straps to get confused with).
Crotch straps are optional and can be either 1in or 2 in in diameter. Usually they're 2 in can help to keep the whole package secure to you. You'll find with a good fitting BP/W that it won't roll on you at all. With normal BC's you roll and your tank sorta delays then rolls with you. This is because you slide in your BC. With a BP/W you roll and your tank and whole backplate immediately roll with you; you're truly one unit with your equipment.
Here's how to set up and fit a Hog Harness:
Hog Assembly and fitting
As a note, with the BP/W comes the DIR concept that most people will mention or push onto you. It entails a different regulator hose and gauge set up which most Basic OW students are unfamiliar with. It's very popular but NOT necessary.
I've seen plenty of Bp/W divers who sport the usual primary reg and long hose octo route
or even a primary reg and Air 2 set up.
Some go with wrist mounted computers and small air gauges or console computers.
It's all up to you, you'll have to use your imagination on the set up of your BP/W.
It can be a little daunting which is why I strongly suggest making friends with a BP/W diver who can mentor you in possible uses and styles with which to set up your BP/W.