In Europe, generally paracetamol (brand name Tylenol in the US) is recommended for headaches / the common cold / flu, and ibuprofen for muscle aches / inflammation.
For something more severe, they’ll recommend taking one type of painkiller, waiting 2 hours, taking the other, then 2 hours later repeating the process.
Asprin is has mostly fallen out of usage as a painkiller, but is sometimes still used for heart / blood problems.
These painkillers are out of patent, so there is never a good reason to pay more for a fancy brand.
That’s long been my approach with the starting meds reversed (ibuprofen, then Tylenol if needed). Acetaminophen/paracetamol’s therapeutic dosage is much closer to the amount required for liver toxicity than Ibuprofen’s is for kidneys, so I think it’s better to start with the lower-risk medication. If I’m in the middle of a multi-day episode that’s well-managed with just one medication at the regular dosing schedule, I will often alternate between them.