I always wear glasses when riding my bike outside as a bit of protection from anything that could get into my eyes. On overcast days, I have some lighter colored sunglasses, though sometimes I just use my regular glasses.
As for sport sunglasses for cycling and running, I do not have a specific brand to recommend, but I have had good success with a wide style that protects the sides of my eyes from glare and wind.
With long hours outside training for long distance triathlon, protection from UV rays is also super important. I have read that not all sunglasses offer good protection, and to look for UV 400 or greater. There is such a range in the cost of sunglasses, and I’m not convinced that you need to spend a ton of money for good quality, but I haven’t looked into this in detail.
I have learned recently that polarized lenses may be nice, but that they are not more protective for your eyes. Polarized lenses have a coating on them that block glare. This can be really great for water activities to see into the water, and some other activities as well. My current sport glasses are not polarized, and I think I may prefer them that way; though my everyday ones are polarized.