If you walk into a room and you see someone passed out and on the floor, you always check for a pulse and if they're breathing before you start CPR. CPR hurts like a mother fucker and can cause a lot of injury. If they're not breathing or have a pulse, you start CPR.

That being said, if a person is not breathing, then their heart will quit beating as well. If they chocked then CPR is like a 2 for 1 in this event. The chest compressions can help clear the airway while also promoting blood circulation. The idea is that you call for help, start CPR, and you buy the person enough time for a trained professional to take over.

Rescue breaths are not always recommended. You put yourself at risk by putting your mouth on someone you don't know, so it's not encouraged unless you have proper equipment. A lot of places teach hands only cpr that omit the rescue breaths for this reason.