" I want to make a detail itinerary and follow it to the letter"

Good luck with that.

Do not hesitate to contact any of the travel providers people here have used. Read trip reports. Check out photos, etc. Some of us have gone the car and driver route, others have taken trains, some have done a bit of each. Contact the providers used to get an idea of budget. Don't worry about telling someone their itinerary is too expensive, they can find other options. Don't forget to include some relaxing time, or doing something you love....we spent half a day in Delhi in someone's home for a private cooking class.

You have plenty of time to plan for February 2015. Take your time to decide what's going to work best for you.

We took our 3 week trip to India in November 2013. In the three weeks we covered Delhi, Udaipur, Jodhpur, Jaipur, Agra.. and Varanasi via Lucknow. .....We received much useful advice from the Fodor community in this thread: http://www.fodors.com/community/asia...l-in-india.cfm . ..
I would also like to add that my must see cities in retrospect would be in this order: Unmissable are Varanasi for a unique experience and Udaipur with its beautiful lake and more peaceful vibe., Interesting and different Jodhpur the blue city and Agra for the Taj and the Fatehpur Sikri. Jaipur and Delhi fitted the trip but are most memorable for hectic pace and hassles. Our trip report is headed "India in November"..http://www.fodors.com/community/asia...r-400688-2.cfm..
I would say research and prioritise your sites and work from there. We found in advance some good flights and trains that left early. En route we booked several good drivers and very good prices through our hotels and one directly through the company the day before departure..Happy to answer any questions...Good luck.