Please help regarding methods of transportation

Hello,
I'm new to this forum and am currently planning a trip to India. I was wondering if anyone with experience traveling within India can offer some advice regarding the fastest and most efficient ways to get from one place to another within India.

My planned trip so far (3 week long trip):

Leg 1: Delhi (Agra side trip) ---> Jaisalmer

Leg 2: Jaisalmer ---> Udaipur

Leg 3: Udaipur ---> Mumbai

Leg 4: Mumbai --> Goa


If anyone has experience in traveling any of the above routes, could you please indicate the most efficient way to travel such routes (such as train, plane, rental car)? Thanks very much in advance.

Go by train, on the most expensive class you can afford. Travel at night if the distance allows it. You will have a great trip.

Tim in England

Of course fastest would be by air wherever possible.
Delhi - Jaisalmer can be done by train comfortably.But if you wish to travel by air, take a flight from Delhi to Jodhpur and from Jodhpur take a car (one way around 4hours)to Jaisalmer.This is the fastest way.(you can also take a train form Joghpur to Jaisalmer)
Jaisalmer to Udaipur is by night bus or by car.

Udaipur -Mumbai is better by flight.
Mumbai to Goa is better by flight but during season it is difficult to get seats.