You've got to make sure your shoulders aren't stiff when you start a chest or bench press workout. That's the best way to have bad muscle recruitment and improper mechanics. You also want to increase blood flow to the area. This will increase the sensitivity of all the shoulder girdle muscles to the neural drive.

Do a superset of two exercises: the band shoulder dislocates and weighted shoulder circles. I like to use bands for the shoulder dislocates since it's much gentler than using a stick (which is often used by Olympic lifters). The band tension also creates some muscle activation which makes it more of an active mobility movement. That means it's going to be more transferable to lifting.

Always keep your arms straight. As you get better at it, grab the band with a narrower grip to increase tension. If you feel a sore spot at any point in the range of motion do slow partial reps or isometric holds at that position until the soreness subsides.

For the shoulder circles, try using both small and larger circles. No need for a specific ratio, just play with it to get the most thorough effect possible. Do 8-12 reps in each direction. Start slowly at first and gradually get faster as you get more comfortable. While you don't have to go super slow, still control the movement, don't do a crazy windmill.

Related:  The Cuban Press for Shoulder Health

Related:  The 10-Minute Bench Press Solution