Both the dumbell and barbell benchpress use a combination of mainly your triceps, pectoral muscles, and anterior deltoid to get the weight up. So the muscle that you target predominantly depends on your technique and form when executing the movement. During the concentric 'push' part of the movement do not lock out your elbows or extend your triceps all the way. You want to work mainly your chest, not triceps, and want to maintain constant tension on your pecs.
Ensure that the dumbell or bar is in line with the centre of your chest, not over your shoulders at the bottom of the eccentric movement so that you are not using your deltoids to take tension off your chest. The lower you bring the dumbell down, the more tension you put on your pectorals. So go low - just watch your rotator cuffs.
Before you start your set pull your shoulder blades together. This will isolate your chest more and take strain off your shoulders. But most importantly GO LOW when you bring the weight to your chest and never bounce the barbell off. To put more tension on the pecs rather pause for a moment at end of the eccentric movement.