which type of body armor cops wear?

There is no standard answer because there are several brands. Some departments supply them, some departments give an allowance and let the officer pick one out themselves. Other departments may not help at all and the office has to get one on his own.

The vests also come with different ratings. The higher the rating, the thicker and heavier it will be. That too is a personal choice for most officers.

A rubber codpiece.

Kevlar?

bullet proof vest