Gazebos are typically free standing. You might try using that as a base and adding screening. Also, do you have Menards in your area? They have a lot of building kits for all sorts of structures.

A lot depends on the look you want. We're also doing a screen porch and will use a composite (not sure which yet) but the type that is interlocking and looks like T&G after install. You can't stain a PT deck immediately so it will have to weather as is for a while - how long I believe depends on how much weather/sun exposure it will get but I believe a year is recommended. Will you be screening underneath the PT flooring to keep bugs out? How will it be fastened? Will they do a blind system so you don't have to see nails in the boards?

Okay: This is what I came up with! Of course, the way you use this space is EVERYTHING. I created two separate seating areas - divided by a "dining" area. One being an outdoor sectional which could be around either an additional fire pit, coffee table, or even ottomans. Near the fireplace/TV is a teak set - a sofa, two chairs, and coffee table. It also depends if you plan on bringing a grill onto the porch as well! Below are the exact pieces I used in the layout:

I think all the ideas that I've read in response to your question are great. You have a lot of things to think about. Is it on the main level of your house or on the lower level? Upper level will certainly block light coming into the room(s) it overhangs, Do you live where you will use it all year long, or just in the milder weather? When there's a really heavy downpour or several days of rain, how does the water flow around your house and patio? Will it be just screens, or will you put in windows so you can use it all year long? That will make it heavier and might need more support at the bottom. We bought our house 6 years ago and the screened-in porch, built on top of the bluestone patio, was already here. It is on the lower level of the house so the roof doesn't shade the main living areas. Although I would have loved it on the main level, I have come to the realization that it's better on the garden level. I have a beautiful wisteria plant covering the roof that can be seen from the dining room window. I believe there was a cement patio originally. The previous homeowner, who is a Master Gardner created a beautiful garden in the back yard with 3 terraces and a stone walkway all through it. Up against the house, she covered the original cement patio with bluestone slabs and then continued it out into a nice large patio. The stones inside the porch have cement between them but outside the porch they have dirt. Even though there are weeds in the section with dirt, I'm sure it was designed that way to let the rain water drain away from the base of the porch. Our house sits on sloping property so the rain runs down the side yards and out into the garden. All the gutter downspouts empty into drain pipes that then run underground until they get to the back yard where they drain into the garden too. All this helps to keep the water away from the base of the screen porch. I get a little water seeping in, in one corner where it's attached to the house, if I don't keep the gutters clear and the overflow from 2 stories up, falls directly into that corner. I use the porch from April to October. It faces east and is a wonderful way to start the day, with the morning sun streaming in. Good luck. I'm sure it will be awesome!!