For the first timers, it's best to visit Goa in Nov- Feb to make the most of the best season and Goa vibes. If you like some peace and quiet, try offseason in Mar, Apr or Oct. If you want to explore the beauty of Goa beyond beaches, try monsoon season for hiking and greenery. Hope this helps.
It depends upon what type of goa you are interested in.. if you want to have all the party and nightlife, fully vibrant and crowded goa.. then November and December are the best times around Christmas and New year times.. On the other side.. if you want to see the serene natural calm side of goa.. least crowded by people.. then you can plan for goa rest of the year once the Christmas and new year is over..