When buying children's glasses, one of the things to consider is the frame material. Generally, plastic frames are preferred over metal for younger children. The reason for this is that metal tends to bend more easily and gets out of shape; the nosepads in the middle of the frame also can fall off. If metal is chosen, the "flex" frame is better. Metal frames frequently come with a "cable" temple that wrap around the ears so that they stay in place more snugly.
For older children, metal or plastic will work. The nosepads may actually help to keep the frames up higher on kids who have a flatter bridge. However, frames with no rim ("rimless") and partial rim ("semi-rimless") may not be suitable for older kids and tweens, but may be ok for teens.