The most economical way to travel would be to take the train and the cities you want to visit not THAT far from each other. Delhi and Agra are quite close (like 2 hours on the express train) but Delhi-Mumbai and Mumbai-Goa will take like half a day or an overnight train. The train times vary, depending on which train you take.
The Indian Railways web site can be a little confusing but you'll get the hang of it. I found it incredibly useful for looking up train schedules. You can look up the schedules on the Indian Railways web site:
http://www.indianrail.gov.in/inet_metro_trns.html
To get an idea of the different classes on the trains, check out this website:
http://seat61.com/India.htm. The pictures are pretty accurate.
The only flight I took in India was from Delhi to Cochin; because that train would have taken 2 days!
Jet Airways Visit India pass of 4 coupons for $500 seems a fair price to me. I guess it depends on how much time you want to save. Some other airlines to check out are JetLite(formerly known as Air Sahara), Air Deccan, Go Air, IndiGo Airlines, SpiceJet, Jagson, and Kingfisher Airlines. I bought my flights when I was in India and I had some problems purchasing the flights online but its easy to go to the airline booking office or a travel agent.
I hope this helps in making the decision whether to take the train or the plane.
PS There are tons of places between Ahmedabad and Delhi that are worth checking out; like Jaisalmer, Jaipur, Udaipur, Jodhpur (eh, maybe not), etc. Trying to fit all of these in for a 2-3 week trip may be a bit ambitious.