It could be any of the things listed above. But unless you have any knowledge on what your looking for/at, your going to need to have someone else fix it anyway. I know wanting to save money but, in this case, bring it to a reputable shop and pay the diagnostic fee and KNOW that the problem is resolved.
But if you insist on trying to fix it yourself... Here's a FREE thing to try. If there is indeed a heat shield rattle or even a catalytic converter with a loose element inside, it will not only rattle while running, it will if you hit the exhaust. So try this. Wait til the car is cooled off, jack it up, crawl underneath the car and proceed to bang the butt of your palm against the exhaust pipe in a few places to see if there is a rattle. Having had both the heat shield and converter element break free on different vehicles, I can say that this will help narrow down the possibilities. This video shows what can rattle in a converter.