Should I use Baltic Birch for stairs?
I don’t see an advantage of using hardwood veneer plywood over spf veneer plywood, unless it’s going to be your “finish” layer. 

Yes, thicker is better, but required thickness is a product of span, (how far apart the stringers are located).

Those numbers (48/24 for example) stamped on the plywood mean maximum span for roofs followed by maximum span for floors...but that is for subfloor, not finish floor.