Should I stain wood then use acrylic or vice versa?
DeAngelis,
  In my personal experience, I have had the most success with this type of project by applying a water-based stain first, followed by the acrylics, and lastly the sealer coat.  You must ensure that the stain you are using is water-based, as opposed to oil-based in order for the acrylics to properly set and adhere. In your order of operations, definitely do the staining process first, before the acrylics, otherwise the stain will affect the color and appearance of the acrylics, just as it is doing to the wood itself.