MarkCK - STCW is a certification, it stands for "Standards of Training, Certification and Watchkeeping" and there are various levels, but the basics are now required for most paid positions and have therefore become an international prerequisite.
intoliquid - I would do the courses at home. I have seem training offerred in Antigua but at a guess the scheduling and pricing won't be as good as at home. From my sessions (at the bar) with crews and officers of megayachts and just plain 'ole vanilla big yachts, they are often looking for crew to fill in the non-specialist positions on their boats. These positions pay (not much, but they do pay) but are limited to those with qualifications.
Your chances of getting a position which doesn't pay but offers bunk & board are much better but those boats will be normal sized yachts. Often they will take on crew for long passages or to cover for a guest/crewmember who didn't show up. In those cases you would have a lot better chances if you could share watches or cook or perform some specialized task.
works for unpaid positions, but crew finders as mentioned above will point you at the commercial side.
The STCW is only worth doing if your goal is to get your entry ticket to crewing on larger yachts.