Rajasthan is the State that encompasses the 'golden triangle' of Agra, Jaipur, Udaipur, Jodhpur etc. - the princely state of Moghul architecture that is the perfect introduction to India.

There is nothing truly historic in Delhi that is also really good, but yes, if you demand historic then The Imperial is the best. personally, I would stay at Aman Delhi.

With 'historic' in mind, coupled with the highest standards of service/food, I would then recommend the following:-

Jaipur - The Rambagh Palace (exceptionally well managed by Taj)

Agra - The Oberoi Amarvilas (nothing else comes close - a miraculous place)

Udaipur - The Taj Lake Palace (because you want historic and it is unique. I would save Devi Garh for a lunch one day - it's doable if you get the hotel to drive you).

Jodhpur - do NOT miss Umaid Bhawan Palace - it will blow you away.

The hotels can all arrange car transfers & airport transfers, but as this is your first time, you may want to book everything through a tour company, like Greaves Travel, who are very good indeed - http://greavesindia.com/ - just don't listen to where they want you to stay - insist on what YOU want to do!