To be clear, the only thing about a BP that would make you have to have an STA is if the BP does not have slots for tank straps. Dive Rite and DSS BPs do have slots.
What tbone is talking about is that if you use a Dive Rite wing, you might want an STA, whereas the DSS wings have built-in stabilizers that ensure the tank don't roll or twist.
If you like a Dive Rite wing, another option is an OMS Soft STA ($15), which will do the same thing as the DSS built-in stabilizers, but not give you the extra weight of a normal metal STA.
Also, there is nothing wrong with mixing and matching brands of BP and Wing. I have 5 wings and only 1 of them is the same brand as the BPs I use (and I pretty much never use that wing any more).
For back plates, I would say the main thing is to make sure it has slots for tank straps. Most do, but there are some that don't. If you want light weight, aluminum, skeletonized stainless steel (e.g. the Dive Rite XT Lite), and Kydex are all between 0.5 and 2 pounds. Aluminum is the least expensive. Kydex is the most expensive.
For wings, there are horseshoe shapes and donut shapes. The trend (in my limited experience) seems to be towards donuts for single tank diving, as most manufacturers newest stuff is donut shape with some not even offering a horseshoe shape.
Some wings have built-in "roll control" - the tank stabilizers that I mentioned earlier. Some do not. They are nice, but depending on price, you might choose a wing without and use a Soft STA for $15 (
https://www.divegearexpress.com/oms-soft-single-tank-adapter). Or, some people use Dive Rite wings with no STA at all and say they have no problems at all with the tank being stable. So, if you wanted, you could try a DR wing with no STA and add one later, if you find you want one.
Most wings have a zipper giving access to the inner bladder, in case you want/need to fix a leak (say, from a puncture or a pinch flat). Some do not.
My personal preference for single tank diving is a donut shape, with built-in stabilizers, and a zipper so I can patch the bladder, if necessary (which I've had to do and is pretty quick and easy).
If you go with a BP/W, you'll also need tank straps (aka cam bands). I started with "normal" cam bands and found them to be a pain to use when switching tanks on a pitching boat. I tried Highland Quick Release tank straps and didn't like the way they worked all. Then I tried cheap ScubaPro-style Quick Release straps and love them. $20 each from here:
https://www.divegearexpress.com/tank-strap-quick-release-with-s-s-hinge-buckle
Good luck!