If you want to make it best then go after coz in mansoon all beaches are closed for swimming and if you are in goa and had not into sea it's a sin. And monsoon is off session in goa so you will not able to enjoy that much.
There’s different phase of Goa and both have their own beautiful sides, so you can go to Goa in the winters and meet the Goan Christmas party vibe, full of people around with lot of crowd in the beaches and clubs.The 2nd side is during the starting/ending of monsoon when Goa is in it’s utter peace, minimal crowd and all green beautiful nature around.
Choices differ from person to person!
January or February is fine. You can also go in the month of December, just it would be way to crowded and costly then. So it's better to have a calm, comforting and pocket friendly trip in either Jan or Feb.