Hi Caesar,
Welcome to the Moms Panel - and thank you for your question! For the voyages to the Bahamas and Caribbean islands, personally I prefer to cruise in January, May and September. These months are typically considered "off" season, and therefore the rates tend to be a bit better.
January can be a bit of a gamble on the temperature, as it is probably the coolest month in this region.
May is an ideal time for weather, but is probably the most popular of the three months I listed. I absolutely love the rates and hot weather that
September offers, and although this is during hurricane season I don't hesitate to plan vacations during this time.
As for the passports, I highly recommend them. You can read more about the requirements
here.