I use those 4' orange electic fence stakes from home depot (about $1 a piece)for lots of things in the yard & gardens. Pound it in the ground and then slide the PVC pipe over it and into the soil a bit. Set out several of these with holes drilled in the PVC pipe and string wire through them to make a fairly sturdy, portable & cheap trellis. I use these stakes to build easy fencing. I use plastic cable ties to secure wire or plastic mesh fencing to them. Because I dislike the orange and it stands out like a sore thumb, I paint my stakes black. Pound 2 rows of these stakes in the ground about 4' apart and slide each end of a flexible PVC pipe over them, making an arch. Cover this with garden cloth or plastic to protect plants. I "sew" the fabric to the pvc with fishing line. If you are using plastic, cut some flaps in it, to keep it from blowing away in a big wind. I use them to brace non secured retaining walls. At my old house I built a raised bed using them to hold the lumber together. I drilled holes in the timbers and slid them over the stakes, then I lined the interior side with heavy plastic.

I would put an outdoor fireplace in now during the construction because I'd think it'd be pretty simple to do if you backed it up to your interior fireplace. I'd also run water, gas, and electricity to the end of the patio(probably on a corner so as not to enclose it too much), too bad the slab is already poured, oh well you can still run it around. Then I'd build in my outdoor kitchen facing out towards the backyard on the corner opposite where most of your usable backyard space is for flow reasons, and so you can see that future pool while you are cooking or anywhere else under the patio, and I would also consider putting a built-in raised bar to sit at on the backside of the grill, so that the people sitting at the bar could see the big screen over the fireplace. Then, I'd get some really comfy furniture that could handle being under a covered patio, and place it near the fireplace, and I'd place a big screen plasma tv over the fireplace(so you need electricity, cable/satelite, and some type of mounting), and don't forget to build some type of storage area for all of the components that go with the tv. And, then there's lighting....make sure that you place some over the grill and bar area and maybe a nice outdoor chandelier in the center of the room, and of course you probably need a couple of fans as well. And, personally I wouldn't do a wall at the end of the patio. Have you ever seen those houses with the really nice columns at the end of the patio area???? I'd do some nice columns at the end, and have some sort of bars or something running around the perimeter so that I could attach some nice flowing fabric and also some mesh that could be pulled across the rods. You could use the mesh for the bugs when necessary, and use the fabric for inclement weather. Make sure you vent your grill since it'll be in a covered area. Hope you have the budget!!! We're working on our pool and outdoor kitchen now, the covered patio and big screen will have to come later.

I’m afraid since the roof is so high, people under the roof would still get rained on because of the openness of the ceiling. Would a roof this high shield rain and or wind? Even sun?

Yours looks like a charming space. No mention of the directional orientation, but perhaps you have too much shade. That would cause the moss and moisture issue So, you need sun and drainage with shade areas to relax and dine. We solve that with trees, umbrellas and a pergola Facing SW we have generous sunlight so the patio is dry. Here’s our space https://youtu.be/lOAwXzKfTxY