because you want a 1" gap between country and board I would use at least 1/2" (12mm) thick wood so you can make some kind of pins in it to keep it " hover" above the backboard.
both ply and solid would will work fine, but plywood has glue so it will dull your blade faster then solid wood.
how are you going to finish the wood, with colors or paint? or just with lacker?
if you are using lacker I would try to get all kind of different wood types so each country has an other type of wood.
my advise, go to a floor company and buy all kind of different types of wood.
solid wood floor panels are almost 1" thick. maybe the can plane them down to 1/2"?
I have a wood floor company that does that for me.
I would use the Flying Dutchman UR#1 for detailed lines but the UR#3 will do just fine also.
also can use the TC#1 blade, but I think the UR just makes small turns easier.
can't wait to see pictures