Unfortunately, in these perilous times we live in talking to law enforcement officers doesn't seem to have any potential benefit. The source of this problem is probably the fact that police are allowed to lie to you, but lying to them is illegal. Police will sometimes lie to you and say you're not detained or under arrest so your right to remain silent does not apply. They are either ignorant or lying to you, your right not to incriminate yourself is ever-present, don't fall for that tactic.
Remember, it's your choice whether to talk to them or not, and if you insist on opening your mouth, try to make everything you say a question. Some of my personal favorites are: Is this a consensual conversation? Am I being detained? What is your name and badge number?
It's also important to record your interactions with any public servant, which includes police. This is because courts are much more likely to believe their fellow government employees than you.
This video from 2015 proved allegations that Jeff Gray (the camera man) forcibly grabbed records (MSDS sheets) from a school administrator were in fact false. The administrator had illegally denied Jeff access and later made these false accusations, but Jeff was recording the interaction and used that evidence to prove his innocence.
As far as police lying, it happens all the time. It's part of their training, and they most likely are very good at it since they do it for a living. However, if you're recording them it can be a huge problem for them, especially if they are attempting to do something unethical in the hopes of making a quota. They may lie to you and say they can arrest you for recording them, like they did with this attorney.
Of course, police administrators deny these quotas exist, but several former officers have blown the whistle on this unethical practice, and departments have been forced to pay settlements when caught engaging in them.
Police can arrest you for refusing to sign a promise to appear (citation) because when you refuse to sign you're basically telling them you'd like to go before a magistrate immediately to settle the matter. The choice is yours whether to do so, and I don't recommend arguing with them.
You'll have to ultimately make up your own mind how to handle police interactions, hopefully this information will help you make a wise decision on how to proceed should you find yourself involved in one.