Final answer:
For non-layered hair that is at least shoulder length, the French braid is the most suited style as it neatly incorporates all the hair and makes it lay smoothly.
Step-by-step explanation:
The type of braid best suited for non-layered hair that is at least shoulder length is the French braid. This style is versatile and can handle hair that is all one length, making it lay smoothly and uniformly. The French braid starts at the crown of the head and includes sections of hair added incrementally as you braid down, which helps to keep the layers or lack thereof neat and contained.
Options like the fishtail braid and box braid may also work, but they do not typically handle non-layered hair as gracefully as the French braid does. The Dutch braid is similar to the French braid but has a more pronounced 'popped out' appearance which might also be suitable, depending on the desired style.