Sports sunglasses (not ski goggles) can make your workout more comfortable because you won't be squinting. A good pair of sports sunglasses protects your eyes from the sun and wind, as well as from flying debris, which is especially important when biking outdoors.
Most sunglasses that bill themselves as sports sunglasses are lightweight and curve to fit the head snugly. But there is a continuum of both quality and price, and you need to find your place on it. You can buy basic sunglasses for a few dollars and wear them for a workout, but they probably won't stay in place without some sort of strap. Sports accessory makers sell sports sunglasses ranging from Champion's $25 model with water-resistant coating to styles costing $250 or more.
For runners, the best sunglasses are lightweight styles with frames that hook snugly over the ears and don't bounce or slide around on the face.
Try different styles to find what model fits your head and face, and don't wear sunglasses in a competition that you haven't tried in training.