Hey, I wasn't expecting to see my name when I clicked this thread. Thanks, NH. :^)
It sounds like you have exactly the right idea about what you want a background to do, it's just a question of thinking what's best to add. I always sketch a color, rough version of a design before I start drawing anything carefully. Usually -very- rough, just detailed enough to plan the layout, pick my six colors, and figure out the foreground and background elements. That helps a lot.
Think of something that naturally belongs with your main design and then stylize it so it's less important, less bold, but helps the overall composition. Avoid any straight edges or awkward cut offs. Avoid making your background more detailed than it needs to be. A little bit of shadow or shine, or a different texture can make your main design pop, so always try out a few ideas.
I've learned a lot by looking at other designers. One of the reasons PatrickSpens and RamyB print so often is they're great at adding quite minimal backgrounds that elevate their designs, and make them feel wearable and interesting. Walmazan, SeedUVPain and bassanimation are all very good at that too, often with more complex background elements. Lucky1988 does some amazing things with his framing.
There are many designers here that have helped me figure out what works. I've certainly had my fair share of backgrounds that didn't. ^_^