It's true that many people don't find Tylenol (Acetaminophen/Paracetamol) very effective for pain relief before surgery. However, after surgery it can be very effective, if taken regularly, in the correct therapeutic dose.
That dose is 1,000 mg, 4-6 hourly, to a daily total of 4,000 mg. You need to check, to make sure that none of the other medications you are taking contains Acetaminophen. If they do, add their amount to your calculations of daily dosage and reduce the amount of Tylenol you take. You do need to take the Tylenol regularly, to keep up the level in your blood.
Ibuprofen and other NSAIDS are primarily anti-inflammatories, not pain relievers. They carry the risk of gastric bleeding, so should be used with caution, and never long-term. Never take them on an empty stomach and stop taking them if you experience any gastric symptoms. They also have an effect on your blood, as they work on your platelets, which can make you more inclined to bleed in other areas as well. That's why you are asked to stop taking them before your surgery.
A recent study has shown that they can also have other ill effects as well:
NSAIDs Diclofenac. ibuprofen increase risk of heart problems: new study
It disturbs me that NSAIDS are available as over the counter medications, as they should always be used with caution.