For my mom's 80th birthday quilt, I made the front out of floral fabrics and the back was mostly all cat fabrics with a strip of fabric, different pieces sewn together, from the front. Plus one or 2 of the cat fabrics had both flowers and cats on them. I rarely, okay never, coordinate the 2 sides together. I like an unexpected twist on the back - even on wall hangings. I do make bindings that play well with both sides but I use a dark binding on quilts - like a picture frame.

I try to use up some of the Large yardage pieces of fabrics I have. If nothing really goes with the top then I use off white backing fabric.
Since I give away most of my quilts, I don't like to Spend money on the wide backing fabrics.

I wait until I have my quilt top complete and decide on thread color to quilt as I quilt all on my Bernina 440QE then I can match thread accordingly and sometimes it is fun to pick a certain print design to use as a pattern for upside down quilting

I almost always pick a neutral. My sister has some very wide ones in tone on tone. I "shop" at her house all the time.

For the quilt mentioned in the project that started this thread, I would keep my eye open for a large scale print with some color, but with a white background and some black in it. I often love to make the backs, because I can get as creative as I want. I'll follow a pattern for the front, but the back can be much simpler, and only have a passing acquaintance with the front. They usually are very simple, and in some cases I like them just as much as the front. I keep my eyes open for sale fabric that I think would make good backing, and snap it up. A lot of my quilts will have at least some of the colors that I go to all the time, so a fabric that contains those will always be useful for me.

I do as Tartan said.