The lab coat is your first protection if spill occures, and protects your private clothes from contamination.
Instruction for lab coats (pdf)
People use gloves to protect their samples from contamination from themselves, and more importantly, People use gloves to protect themselves from hazardous samples or chemicals. Gloves shall always be removed when you touch areas that other people touch without their gloves, like door handles, keyboards, normal lab working Space, offices etc.
Remember that your ordinary gloves is not an all-round protection. If you work with high-risk materials/ chemicals you should concider the quality of your gloves.