Robert, still not clear, are these backgrounds solid boards or fabric?
Either way, regular matt paint will be very easily smudged and stained with normal studio use, so if you're forking out a lot to get these done, make sure they're properly sealed with a matte spray after painting.
A gloss finish will be easier to clean & maintain and probably won't need separate sealing/varnishing but obviously it will reflect your lighting - this can be used to great effect and you will get more texture & contrast than with a plain matt or satin finish but it will also be less versatile than a background that can be lit from any angle without worrying about the reflections of light modifiers and reflectors being visible.
Personally, I usually paint with all matt paints (cheap 5L cans of primary colours that I can mix), then use a high gloss varnish on the areas I want to reflect and seal the areas I want to remain flat.