We did a private tour arranged by Enchanting India 3 years ago and found the experience amazing. The local guides booked for you will tell you all sorts of interesting things about life in general in India and although the major attractions, like the Taj Mahal, palace of the winds, red Fort in Jaipur will be very memorable it is the little things that make the biggest impact, beautiful ladies in Saris riding pillion on a motorbike, with tiny children, Water buffalo being escorted to a muddy pool in the morning and back again at night, The beautifully adorned and painted lorries, starlings that look extremely exotic. One of the places that isn't always included in these trips is Udaipur, the lake is very beautiful and some lovely sights round there. We also visited Shimla as an add on, highly recommended.
Like many others I'd advise being vegetarian for the journey, DH and I had no problems with our digestions at all.