Size really depends on the size of the shelf and the spacing of the umbrella sleeves. We found that the 11' diameter umbrellas were too large, and the 9' ones work well for our use.
I can't remember the brand names off hand, but we've tried several, and most of them are pretty comparable. Some have slightly better or worse lifting and tilting mechanisms, and IME the simpler the better. The more complicated ones seem nice at first glance, but they tend to be more problematic in the long run.
+1 on Sunbrella fabric, often costs about 2x as much as the cheaper fabric versions from the same brand, but the fabric doesn't fade or deteriorate nearly as fast as the cheaper stuff (especially here in the sunny desert).
You're right on track about aluminum instead of wood for the pole. For the ribs, I've found that fiberglass holds up way better than aluminum. We've had a few bad wind gusts toss the umbrellas and bend/fold the aluminum ribs, but never had an issue with the fiberglass, despite my kids abusing them pretty badly.