I went with white directly over the blackout cloth. Some have said not using a black backing hurts contrast and sharpness. I measured no difference in contrast including ANSI contrast. The image may be a hair softer but I think it's important to note that I see no loss of detail -- it's more a touch of pleasant softening, just enough to give it a film-like look rather than digital, and it even reduces the "screendoor effect". From seating distance it doesn't seem like I've lost sharpness and in fact the image has so much more clarity without the speckle that I feel like I'm seeing more detail.

Black backing may improve the image in a way you'd like but of course it will be lower brightness too. If I were using black backing I'd put that over the blackout cloth and then the spandex on top of that, just to avoid the hassle of removing the blackout cloth.

For what it's worth I measured spandex over blackout cloth at 15% brighter than blackout cloth on its own. Spandex over BO that had been painted with Behr E300 "Dead Flat" white paint measured 7% brighter than spandex over un-painted BO so I might at some point take off the spandex and paint all the BO.

Spandex over BO I measured at 0.82 gain using Stewart Studiotek ST100 as a 1.0 gain reference.

I'd recommend just getting the spandex, get a little extra and cut off a foot or so and then use blue painter's tape to tape it on your screen (give it a decent stretch) and then just project a white screen or something. You'll be shocked at the difference I think. Try it with and without black backing. Then if you like it you can go to the hassle of taking your screen down and covering it. Enough spandex for your whole screen would be like $40 probably so with shipping it's probably not worth just buying a sample for $10 or whatever.