Probably the most widely used medication around is Tylenol (acetaminophen) a.k.a. APAP or paracetamol. It's been around for about 150 years and is on the WHO's list of essential medications needed in a health system. That's a good endorsement.
How does it work? Funny story is that nobody really knows. "The analgesic effects are believed to be due to activation of descending serotonergic inhibitory pathways in the central nervous system" - that's the best answer out there.
It's pretty safe for most anybody without an allergy to it (as with every medication) for any manner of things but pain and fever are the actual FDA indications it has. The one big issue with it is liver toxicity. If taken as recommended on the bottle, it is usually harmless, but still, Tylenol overdoses are the number one cause of liver failure in the West. And unlike some other organs, once your liver fails, you need a new one immediately - there is no temporary liver replacement machine.
Imagine your liver is like a baseball stadium. Y'all seem to like the Giants so let's call it AT&T Park. Normal acetaminophen use would be like a scheduled game and security is there to make sure everyone goes in in an orderly fashion without your outside drinks. An expected crowd shows up and the security is adequately staffed to handle them. But if suddenly they decide to make it the last game of the season and it's free BMW day, the regular security staff is going to be overdosed with people and unable to control them from tearing the place apart. That's pretty much the case. The liver can only handle so much acetaminophen at once and anything extra just starts damaging it to the point where it can start dying.
Over the last few years, you may have noticed "extra strength" tylenol (acetaminophen) has gone off the shelves and/or the doses have been reduced. We used to say that 4 grams a day was safe, but now that's been reduced down to 2 grams a day.
Intentional overdoses are one thing that can be a problem, and warning labels won't help with that, but the concern was the accidental overdoses from people who were taking acetaminophen too frequently or then not realizing it was also in some over-the-counter cold remedies or other medications where it's not obvious. There probably also wasn't much added benefit from the higher doses.
So now we say to check the boxes on any over-the-counter medications you're taking and make sure the dose doesn't add up to more than 2000 milligrams per day. A little over is probably OK but keeping to that will be safe even for people with liver problems.