Double jointed oval mouths (also called a lozenge) tend to be the gentlest type of mouthpiece. They are milder than french links (normally) because of the rounder mouth piece.
If your horse has a big mouth, high palate, especially with a small tongue, thick mouthpieces will be milder because of the bigger surface area where the bit touches the horses mouth. If your horse has a low palate and/or big tongue, a thicker mouthpiece will be more severe as it wont fit the horses mouth as well, a slight movement of the rein and it moves into the horses tongue or bars.
“Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen.” - Unknown