The rail is a rather inexpensive way to travel and you will reach your destination in approximately six hours and 24 minutes. With the main railway station being in Madgaon, which is North Goa; try to take a train that stops at Thivim if you plan to travel to the North Goa beaches like Anjuna, Baga, Calangute, etc.
Avoid renting a car or a jeep and opt for public transport. A scooty/bike can be rented for a day for around INR 500. Split between two to spend reasonably. Remember every penny spent makes a difference if this goa trip plan is based on a budget trip - it's all about spending wisely and picking the right options.
Both taxis and auto rickshaws can be pre-booked, alternatively, you can flag down an auto rickshaw when needed. A scooty (local word for scooter) is a very popular option in Goa and the most preferred mode of transport, not just for visitors but for Goans themselves.