You can really use whatever veneered plywood that looks best to your eye. Oak has a more open grain which takes more sealer to fill but is worth the effort if that's what you want.
Stain is entirely up to you. Birch plywood does not always take stain evenly which can create a blotched look.
What do you mean by "finish this out"? Do you mean the sealer, trim work, or what?
I priced the polyethylene and it was super expensive at around 40/50 bucks a gallon.Is that right?
Do you mean polyurethane? The waterborne types are pretty expensive but go on so thin that they are pretty economical overall. You can get epoxy for just a bit more per gallon but it goes on thicker and costs more but you do end up with a much more durable and easy to clean finish.
I do suggest avoiding oil-based polyurethanes. They are cheaper and offer a nice degree of protection for the money but take a long time to offgass, especially if not applied correctly, and possibly won't even be available by 2011.