For ease of cleaning, I'd put the polycarb on top. Even if the top of the pergola is flat, you could just add some wood spacers to the top side of the joists, and have the spacers get progressively thicker as they go across the top of the pergola: you only need a very slight incline to have the water run off. Using twinwall polycarb might be nice for diffusing the light a little.

Ours is complicated, photos do not show sufficient detail so I'll try explaining. Electricity - I ran PVC under the pavers, daylighting adjacent to one of the pergola columns. The source is from the sub-panel which also feeds our hot tub but has space for additional breakers. Use wide-turn elbows to permit pulling the wires. Our pergola has two perimeter 2 x 12's to support the roof. On the bottom edge of the outside one, I routed a groove and installed rope lighting. Also have made provisions to install a ceiling fan above the table. All electrical is weather tight, grounded and on its own GFCI breaker. Our speakers are located elsewhere. I wouldn't recommend speaker wires and 110 volt in the same conduit. Our Pergola is about the same size as yours, but free-standing. If you offer more particulars about your build perhaps I can offer better suggestions. Hope this helps.

I recently bought a steel pergola kit from Lowes that has a canvas covering over the top. It has two metal weights on each end, but the canvas still flies off if there is a heavy wind. I knew this when I bought it as this was the major concern of all who posted product ratings on the site. Many people on the site said they tied down the sides with rope after using gromets to thread the rope thru. I purchased rope and gromets today to do just that but before I tackle it, I would like suggestions from this forum as to what would be the best way to do it. I am posting a picture of the pergola (If I can figure out how to do it as I am new to posting). Please any and all suggestions are welcome. Here is a link that might be useful: Pergola with Canvas

I would say yes one is enough. Here's ours. This is one vine but it's about 50 years old. See the thickness of the pillars that hold it up? You need something about that strong. The last pic is looking at it from the second story windows. They are messy though, in addition to twice a year pruning you have leaves and twigs that drop all the time, the flowers drop while still moist so they stick to the concrete and in the fall you have seed pods. Btw, the seed pods explode with a loud bang and can be rather startling, especially for guest, XD. But they are heavenly in March, and the scent can't be beat!