Whether you will look handsome with the glasses frames depending on your personal style. Some men do look handsome with some styles of glasses frames, but it doesn't mean these kinds of glasses are suitable for each man. Therefore you should wear glasses that are suitable for your own personal style and they look perfect on you. Personally, I think the full-rim rectangle glasses are very suitable for most men. You can try them on and see whether they make you look handsome or not.
If you want to look handsome with glasses frames, you can try a pair of black wayfarer eyeglasses frames. Such style of eyeglasses frames are very popular among men. They can make them look handsome and young. Or if you want look mature, you can try some golden or sliver metal framed eyeglasses, or horn rimmed eyeglasses frames. Just try on and test it out yourself so as to find the best looking eyeglasses frames.