Always wear some form of eye protection when you're riding! The wrap-around "sport style" sunglasses are nice if you have some high-speed descents or if the wind makes your eyes tear up, but otherwise, anything will do. My lenses are pretty scratched up from years of bug impacts and various other airborne debris.

As for the sweat issue... It was mentioned above, but Halo headbands are by far the best headband-type product I've used. They make a variety of styles; I use the skull-cup one to keep the top of my head from getting sunburned into a helmet hole pattern. Keeps bugs out of my hair as well... Again, find the style that works well for you.

Sunglasses and Halo headbands. Don't leave home without 'em.