Consequences towards the opponent that dont lead to death would be such things as; Broken bones which if used on the opponents arms, legs etc would lead the opponent unable to defend against any further attacks to the best of there ability, certain attacks could also leave the opponent paralyzed both of these after effects would also leave the user unable to cast handseal needed jutsu if aimed around the arm. Attacks do not always have to be powerful strikes, as even the most simple moves such as a quick jab to the face could leave the opponent dazed & confused leaving an opening for the user to strike again.
As you said attacking around the chest area is a far more swifter & easier choice due to the size of your targeted area which has many areas that could cause severe damage such being;
Rib Area - Powerful strikes can leave the opponent with a broken rib cage, this would have the opponent unable to successfully strike back due to the amount of damage caused & trying so would only leave the opponent in a worse off condition than before as it would only further damage that general area.
Chest - The general area of the Chest has multiple effects for the user to pinpoint all in which could aid in a continuous assortment of strikes, you can strike the chest with swift movements which would lead them to fall back & lose balance, it can be easily done by quick jabs or a palm thrust which would be most effective as if would serve both purposes of causing the opponent to lose balance & also further injure them at the same time.
Solar Plexus - Striking the opponent with a forceful blow around this area can cause the opponent to become winded, in this state it is extremely difficult for them to defend themselves due to the sudden impact knocking the wind out of them.
Arm Pit - This area has several nerves which if hit can cause the opponent to lose feeling as either a temporary effect or could even lead to the opponent losing feeling in his arm permanently.
Groin - Possibly the most dangerous section to attack for the male gender, not only could this cause severe physical damage which would render the opponent to simply drop to the floor, it can also cause the opponent to lose stability mentally >.>.