What type of braces should I go for to straighten forward pushed lateral incisors? (Photo)

Your problem is NOT the lateral incisors being pushed forward but rather the central incisors being pushed backwards. The type of bite you have is common in people with an underdeveloped upper dental arch. Because your upper arch is underdeveloped, your lower jaw is set too far back. A very large percentage of female patients with your type of malocclusion also suffer from TMJ Dysfunction and sleep breathing disorders.No braces or clear aligner system will fix everything that needs to be fixed (gummy smile, retroclined central incisors, underdeveloped upper dental arch, retruded lower jaw, etc.) in your specific case. In my office, we would develop your upper and probably lower dental arch, advance the lower jaw forward and then use braces to properly align the teeth. This would be accomplished with a single, comfortable, removable appliance followed by braces. Good luck!