I’ m here to help you ,how to plan your Goa trip.The state is divided as south Goa and North Goa.Now ,if you are planning to spend your holiday in south Goa then you have to get off at Madgaon or Kulem station & if you would like to visit North Goa then you have to get off at Thivim station .Beacuse Thivim station is nearest station from Baga .Baga beach is about 13-14 km from Thivim station. According to your plan you have to decide at which station you have to get off.
From Thivim station about 5-10 min. of walking distance you will get city bus to mapusa. From mapusa you will easily get buses to baga as there is no direct buses to reach baga .
city bus charges : (per person)
Thivim to mapusa:20-30 ₹
Mapusa to Baga:30-40 ₹
If you want to book cab or take a taxi at thivim station it will be very costly .They cost you about 500-600rs to baga.
With my personal experience i would like to suggest you to take city bus instead of taxi or auto.