Looks good. For that length of span, you would not have needed the extra center posts, but it certainly stabilizes that much more.
A poly coat should be fine. With a painted or stained covering, you would have wear and tear, with maintenance. I would suggest you consider using satin or semi gloss, as gloss will present additional maintenance as it wears. One thing I would strongly suggest is an abrasive additive that is available for mixing into paint/stain/polyurethane. It is available in most paint stores and Home Depot/Lowes. It is basically a sand material that will provide a rough surface, thus giving a more secure surface for walking on. As you coat your new stairs, wait to the final coat of the treads and add the abrasive additive to the remaining material and use it only on the tread surface.
Great thread and pictures.
b
