The Goan high season runs mid-November to mid-February: dry, sunny, daytime highs around 30°C, nights cool enough for a shirt. This is when Calangute fills up — book everything, expect Christmas and New Year to be packed and expensive.
March to May is hotter, stickier and quieter, with prices noticeably lower; the sea is still swimmable. June to September is the monsoon — the beach shacks are dismantled, many restaurants close, and the sea turns brown and dangerous, but the inland landscape erupts in green. The October "shoulder" is the underrated month: shacks rebuilding, prices low, weather almost dry.
If you can avoid the Christmas–New Year week and mid-December Sunburn Festival weeks, do.