How large are the signs?

I would suggest a different background depending on the content of the sign, to look good against it. In general, middle tones are best. For small still lifes I picked up some craft foam and faberic squares in every medium tone, and I like light blue, ivory, grey. If the pieces are large, you can at least have a reversable painted backdrop, or a selection of cloths (like bedsheets). Hang two or more layers of colored bedsheet kimd of cloth against a painted black board, held on with binder clips.

You might put the sign a few inches from the background to make a nice shadow, or a larger distance with the background lit separately (that's more work).

OTOH, if you will crop out the sign in the photo (and correct the perspective), the background won't show in the final work. So use grey with gridlines to helpmyou get straight and fix distortion. Mid grey won't confuse your histogram or auto-exposure with extreme values that it tries to fit in, and serves as a known reference for color correcting. With grey that's one click to remove color cast.

I like the idea of using background colors that are similar to the destination. Then you see how it harmonizes or clashes like the cuatomers. So... how about green camouflage, to mimic the out-of-focus ground, sky blue for those seen looking up, and a color similar to the building for signs on a wall.

Note that if you shoot anything you can chamge it in photoshop easily, to (say) bring in a photo of the property. For that, crop the sign so no background, but easy to stick over his photo or play with colored mattes later.

Now, how about lighting? Your constructed stage can have marks or sightlines for where you set up, if not a perminant part of it. I suppose you are already happy with the lighting (nomglare rendering it unreadable) but that's another thing to take up a notch.