Best month for cruise?

[BSDolk]

I would like to do the 7 day Eastern Caribbean cruise with my DH and two DS (ages 4 and 5) next year somewhere in the January - April time frame. Does anyone have an opinion on the best month in that time frame, as far as:

1. Having warm enough weather to swim on the ship and at the beaches.
2. Have calm seas since my DH thinks he is prone to seasickness.
3. Avoiding the most crowded times.

Thanks!!