No matter what you do about the deck, the aging, ragged bushes all need to go. They have outlived any possibility of enhancing this part of your home. Once they're out of there you'll be inspired. I would add broad steps at the door that span the entire width of the sunroom. Jalousies are terribly inefficient. I would replace all of them with new windows. If you want to open them for air circulation, then get sash style windows. If you never open and have good AC to compensate for the heat in a sunroom, you could add plate glass. I would do that even before considering a deck addition. It will mean more to your utility bill and general comfort.

Replacing the windows would be the first priority, solar shades for heat and UV control next IMO. Then removal of all the bushes to see what you have to work with and the only thing to remember if you put a deck along the side of the house it might cover basement windows , maybe take some pics of that side of the house.Yout entry intoe sunroom could be incorporated into the deck.