Hire a car and driver from Delhi itself. You can spend a day or 2 in Delhi, 1 night in Agra and a couple of nights in Ranthambore. The car can take you to Jaipur from where you can fly to Mumbai. As you can see the itinerary is a bit tight. If you want to spend more time in the North, then you should try and take a flight back home from Delhi, instead of Mumbai.