Regarding which consequence gets marked off, the player taking the consequence always decide whether to take a consequence in the first place, and if so which consequence or consequences. So, for example, the player could choose freely between taking one large consequence or several smaller consequences. In the specific case you mention, if a player had a mild useable only for physical stress, and a mild useable for any type of stress, there's no reason not to mark off the specialized one first, assuming it fits te stress taken.
Regarding splitting the stress into two stress boxes, YS202 says:
"When your character takes stress, mark off that box (and only that box) on the appropriate stress track. For instance, if your character takes a two-point physical hit, you should mark off the second box (and only the second box) from the left on the physical stress track. If your character takes a hit and finds that box already marked off, you should “roll up” to the next empty box on the right and check that off. If there are no empty boxes to the right (in other words, the hit would “roll off ” the end of the stress track), the character is either taken out (page 203) or needs to take consequences to absorb the hit (page 203)."
The parenthetical emphasis is as written in the book. You only mark one box, and if you don't have a box at the right position, you either are taken out, or have to mark off another consequence to soak more of the stress. (Player's choice.) At least, that's the rules as written, you are of course free to change them for your table.