The cheapest and easiest way to find plexiglas is to buy a poster frame at a local craft store, such as Michael's or Hobby Lobby in the US. You can often find 2 for 1 deals on these.
Keep your color palette limited. This will create a more unified final product.
Use larger foam brushes for most of the work, but have some small ones on hand just in case you need to dress up some edges. Don't use the small ones for the bulk of the painting, as it looks a bit rougher and takes more time.
Here I'm using the cardboard backing as I paint the plexiglas, just to keep it from getting scratched on the table. Make your fields larger, not smaller, even if that seems out of scale. It will benefit the final product, even if you aren't doing 1:1 battles.
The key is to keep the paint thin. You want to see some brush strokes, and you want to be able to see through the final product.
Here's what the final product should look like. I placed a drop cloth with some chalk marks on it underneath the map behind it so you can see how transparent it will be. The natural cloth underneath brightens and unifies the panel. Of course, when you do this for real don't draw on the cloth; this was done for the sake of illustration.