I might have addressed the problem of the curve facets being so apparent. Somehow I didn't notice it before but the smoothing angle had been set low at only thirty degrees. It's possible that when I last upgraded the SketchUp program the smoothing angle had been reset lower and I didn't notice. I've now reset it to at least ninety degrees and I'll see what difference that makes. If it's not enough of a difference then I'll set the smoothing angle higher again.
Also, one thing I'm finding as I'm beginning SU, is that the circle tool defaults to 24 sides. You can change it in the lower righthand textbox to be a higher number if you like (48, 96, etc).