Hey... There are many ways to move from Ahmedabad to Goa. However, if you like road trips, then you should definitely try it. I found a similar story and I'm sharing it with you. Check the link below. Hope this helps!
https://www.tripoto.com/trip/himalayas-and-hinduism-394780
Hi! The cheapest and most convenient way to get to Goa would be to take a train, for which many options are available. The travel time from train is approximately 20 hours. You can also take to the road and drive but that could end up costing more as you would have to take many halts. the travelling time would also be increased. Happy Travelling!
You can travel by train till Goa, Thivim mostly, and after reaching your hotel / stay, you can hire a scooty to roam around. Its easly available in every corner of Goa and the cheapest way to explore Goa!