We have stacked decks on the west side of our house. A few years ago, we decided to add removable screens to the lower deck. We added permanent screening to the underside of the lower deck (easy in our case because the basement walkout was directly below) and to the underside of the upper deck. Because the main floor deck is a wrap-around, we added a lockable screened door at each end. We decided on removable screens because of the amount of wind and snow we get here in winter. Much easier to remove the cedar framed screens than to replace the screening every year or so.
If any of you have experienced black fly season (tiny aggressive little buggers that actually take a bite out of you and are around in early spring thru to the hot weather), you will understand the pleasure our screened-in deck has provided. We spend many an evening there, watching the local wildlife and enjoying the sunset. The cats love their extra freedom and hang there most warm days.
The only thing I would have done differently, is not to have waited 10 years to do this relatively easy diy project. You will never regret your screened in room.