What is the best pain killer for knee pain?

No such animal. What is best for one, maybe off limits for another. If you had liver disease, i would not take tylenol or acetaminophen. If i had diabetes, hypertension or kidney disease, i would only take anti-inflammatory meds under doctor supervision. So, answer maybe physical therapy, aqua-therapy, an orthopedic evaluation for your custom options.
NSAIDs. Well the best pain killer the the least strength medication you can use to reduce your pain. I would suggest, stretching/strengthening and icing knee and using an ibuprofen/aleve/tylenol medications first. If they don't help, the consider evaluation by doctor fro medications stronger for relief.