You're talking an outdoor space here, not an indoor one. Wood would never be on the list unless you did something like tongue and groove ipe decking. The only suitable floors for a non temperature and humidity controlled space would be porcelain tile, indoor-outdoor carpet, concrete, or possibly vinyl, but the vinyl would depend on the amount of UV the space gets. UV will kill vinyl, or any finish meant for interior use.

Get more bids. We added a sunroom (it seems like eons ago...maybe 2007?) Times were tough and contractors were looking for work. Still, I had to work to find a guy to do it for $30K. I did not have the benefit of having the foundation deck already there, and added electricity out there. My FIL built his own on his deck. He used patio doors for the windows.

I go with the sunroom, too, and here's why. You can build a shed for cheap at some point, and until then you'll probably keep one car inthe driveway, and all the bikes and basketballs in the garage along with the yard and snow tools. The sunroom will make a great playroom while the little ones are little. I've seen that sunroom with nothing in it but a low-pile play rug and Lego. Or balls. Or plastic hockey sticks. Or those big Little Tykes (slide, trikes, trains) Or Hot Wheels. Or dollhouses. Or art projects (easy-to-clean tile floor). Usually just one or two of those. But a great playspace, near you but not, outdoors but not. After they are done with those types of toys, it can be dining space and added living space. You don't need the shed until Boy #1 gets a car. Oops, didn't mean to scare ya lol! Upstairs, I wonder if you can steal some space from the game room to make a reach-in closet for Bedroom 2, and use its walk-in closet to expand the bathroom. 5 boys will need more counterspace, more drawer storage, and (I can't believe I'm saying this, I'm usually a 1-sink gal) 2 sinks. Downstairs, consider eliminating the study closet and adding a shower to the powder room.

There's not much I can do now to add shade for the patio. I've considered various shades and umbrellas for the porch and patio but it just gets too windy at times, plus as the sun sets it gets too low even for a tilted umbrella. I don't doubt that a sunroom like the inspiration photo would be very expensive. My space won't be nearly as tall or wide and I will not have the nice windows shown. I'm guessing I'd have four or five good size vinyl windows matching my the current windows on the house and then a patio door, maybe a French door. For my addition I think the bulk of the expense will come from excavating/pouring the foundation, altering and adding on to the roof, electrical and hvac, and possibly whatever expense comes from relocating the electric meter and sprinkler system. I can DIY most of the interior finishing, but all the big jobs I will leave to the contractors.