My glasses have always been light enough that I'm one of the holdouts for GLASS lenses. But, I now have all the options so Astigmatism, Progressive, Photo Grey, Safety Glass Lenses in Titanium frames. They're not cheap.
As far as keeping them on the nose, I always buy the temples long enough that I can do a full 90° wrap around the ears.
I don't use straps, but the helmet is enough to make it difficult for them to fall off the head when riding.