The American Heart Association does not have FIRM recommendations regarding the use of NSAIDS, but there are recommendations for people with known coronary disease or people at risk:
It is known that certain NSAIDs increase risk of cardiac events (COX-2 inhibitors); there is also good evidence that it occurs with all NSAIDS. Having said that, the current recommendations are to start off with Naproxen since it has not been shown to do this and is considered "neutral" in risk; it doesn't mean that it might not get shown to have the same problem in a future study...
Most physicians are starting with Naproxen or using it after tylenol or tramadol fails.
Thanks for the interesting question.