Yup. Lots of opinions. Just to add. Since you have already negotiated the fare the driver will, for his own interest as well as yours, drive the best route, no need to worry about that. As well, I agree not necessary to tip. A NA custom that I hope doesn't catch on in Peru. They mostly all have a family to feed, cage or not, and feeding a family is a reason to tip? Anyway, not expected and not necessary.

Also, just tell the driver if you have a large bill (as Siempre Viajando says S/.20 or more) and he will stop at a grifo to change it along the way.

I have a worldwide guideline to try to avoid any taxi driver that is waiting at any airport, on the theory they have time to plan and can be pretty sure of getting a pax with important stuff in the bags. We are most vulnerable when travelling because we have all our stuff. Not always possible, but preference goes to a taxi dropping off a pax.