Liliana--hopefully someone else will chime in here. But, as I said before, travel to Anguilla is ferry, either from close to the airport or from Marigot, on scheduled ferries, unless you take a day trip excursion on a boat For St. Barts, you can fly either from the Dutch side airport or the French one. If you're staying French side that would be easier than flying out of Juliana. If you have a tendency to be seasick, flying might be the way to go, as it is often VERY rough on the way over, usually much less on the way back. For ferries, you have ferries from Oyster Pond on the Dutch side and from Marigot on the French side. Those are scheduled ferries, with specific departure times.

As far as overnight on either one, have never done either, so have nothing to add there.