People always underestimate how much there is outside the main Inca circuit and end up wishing they'd planned for more time. Lima alone could eat up two or three days easy if you actually stop there properly. On the car question, Peru's worth doing with your own wheels for a good chunk of the trip. You can rent a car in Peru here
https://getrentacar.com/en-US/peru . Something comfortable handles the main routes fine, and for the coastal stretch south of Lima toward Paracas it makes the whole thing way more flexible. From there you can keep pushing south toward Arequipa and stop wherever looks good along the way.